Timothy Workman, a London magistrate, issued the warrant at the Marlborough Street court after hearing that Mr Levitt was overseas and had no plans to return to the UK.
He ordered that the warrant should not be backed by bail to ensure Mr Levitt was taken into immediate custody once the warrant was executed.
The warrant follows an investigation by the Department of Trade and Industry over allegations that Mr Levitt had acted in contravention of the Company Directors (Disqualification) Act 1986.
Nicholas Hobbs, DTI investigating officer, told the court that he was in charge of the criminal investigation into Mr Levitt's alleged offence.
In reply to a series of questions from Simon Clements, prosecuting, Mr Hobbs said he wrote to Mr Levitt at his London address in July this year requesting an interview.
Mr Levitt replied by letter on 4 August, saying his professional advisers would not be available to assist him until September. The investigator said that Mr Levitt wrote a further letter in September, saying that he had not been involved in any business activity since "early 1995", no longer resided in the UK, and had no plans to return here.
When a summons was issued, it was returned marked "refused", and Mr Levitt's wife had said that her husband had left the UK earlier this year, and no longer resided at the address in north London.
Mr Hobbs said the DTI as a result did not think that the summons could be enforced without a warrant being issued for the arrest of Mr Levitt.
He also confirmed that Mr Levitt's solicitors were not being instructed by him in connection with the matter.
After hearing this, Mr Workman granted the application, saying: "There'll be a warrant with no bail."