Venables, who was convicted of the murder of James Bulger in 1993, was recalled following "extremely serious" allegations, Mr Straw said in response to an urgent question in the Commons.
Mr Straw indicated earlier today that he might break his silence on the reason for the recall but told the Commons "this would not presently be in the interests of justice".
The Justice Secretary said he understood the "frustration" of James's mother Denise Fergus - but mistakenly referred to her as "Mrs Ferguson" in his statement.
Venables and Robert Thompson, both just 10 at the time, snatched James from the Strand shopping centre in Bootle, Liverpool, in 1993.
They walked him more than two miles to a railway line, where they beat him to death and left his body on the tracks to be hit by a train.
The pair were released on life licence in 2001 under new identities.
Since it was revealed that Venables had allegedly breached his licence conditions, there have been numerous reports about the reason he was recalled to custody, including claims that he possessed child pornography.
Mr Straw told MPs: "During the week beginning February 22 this year, officials in my department learnt of a compromise of Venables' new identity.
"Subsequently, information came to light that Venables may have committed a serious breach of his licence conditions.
"He was recalled to custody the same day and has since remained in prison. A parole board hearing will be held as soon as practicable."
Mr Straw said full details of the allegations had not been provided "because the police and the Director of Public Prosecutions have advised that a premature disclosure of information could undermine the integrity of the criminal justice process", including any potential prosecution.
The Justice Secretary was speaking after Mrs Fergus told ITV's This Morning she was "all over the place" after her son's killer was recalled to prison.
Mr Straw said: "I fully understand the concern of James Bulger's parents and the wider public about this case and indeed the frustration voiced by James' mother Mrs Ferguson that insufficient information has been provided to her.
"As I indicated earlier today, I have been giving further active consideration as to whether it would be appropriate to provide more information.
"But, in the event, I have concluded this would not presently be in the interests of justice."
Explaining his decision, Mr Straw said: "It is critical that if charges do follow, it is possible to hold a fair trial - fair for the defence and fair for the prosecution."
The motivation was to ensure "extremely serious allegations are properly investigated" and that "justice is done".
He added: "No one in this country would want anything other."
If any offender on a life licence was charged with a further serious offence, there would be a "thorough review" of the supervision he was under, Mr Straw said.
Under questioning from MPs, Mr Straw said he had seen "no allegations" that Venables had been involved in any incident in which anyone had been killed or seriously injured.
An aide to Mr Straw said his reference to "Mrs Ferguson" was inadvertent and the Justice Secretary apologised for any offence caused.
The aide said: "It was a slip of the tongue. He apologises for any offence caused by that."
Shadow justice secretary Dominic Grieve said Mr Straw could have told MPs earlier about the limited information he was able to provide, as well as given more details about the legal process and grounds of recall.
He also suggested Mr Straw could have given a commitment to disclose more information "once the relevant parole or prosecution decisions have been taken, in redacted form if necessary to protect Venables' identity".
"These could help to avoid the frenzy of speculation that has arisen in this case," Mr Grieve said.
"All in this House will have a shared concern with the Justice Secretary that that speculation doesn't interfere with the course of justice."
Mr Grieve said Mr Straw and Home Secretary Alan Johnson had given different comments to the media which "appeared somewhat inconsistent", after Mr Johnson said the public had a "right to know" what Venables had done to be sent back to jail and would "know all the facts in due course".
Such differing comments do "not help public confidence in the justice system", Mr Grieve said.
He called on the Justice Secretary to explain Venables' licence conditions and commit to telling MPs about the actions taken by the Probation Service so that the public could be assured that Venables had been properly supervised.
"There is now disquiet - including from Mrs Fergus - that this hasn't happened," Mr Grieve said.
He also asked for assurances that the grounds for not saying more were a "practical need to avoid identifying Venables, given his new identity and the possible requirements of the trial process", rather than "a broader creeping advance of privacy rights for criminals which comes at the expense of public transparency".
Mr Grieve said Mr Straw deserved support for dealing with "very difficult ministerial responsibilities" but also needed to explain the circumstances around them.
And he added: "No one needs reminding of the appalling circumstances of the murder of James Bulger - it shocked the country.
"But the role of ministers is not to ebb and flow with media speculation."
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