The Spurs left-back, 30, was arrested after colliding with a central reservation in his car, which was left with three wheels and suffered extensive damage in the accident.
After being deemed fit for questioning, Rose was released on Thursday pending further investigation.
A spokesperson for Northamptonshire Police said: “We can confirm a 30-year-old man was arrested on suspicion of dangerous driving on the A45 in Northampton shortly after 4am yesterday (Wednesday, December 23).
"The 30-year-old has been released under investigation.”
The Sun reported that Rose passed a roadside breathalyser test, but was still taken into custody on suspicion of dangerous driving after the accident.
It is not clear why Rose was in the Northampton region in the early hours of Wednesday morning, with the A45 located near the M1 motorway to the north of the city.
Rose, who spent part of last season on loan with Newcastle United, has fallen out of favour at Spurs since Jose Mourinho took charge and has not made an appearance this season, with the Portuguese manager speaking publicly of his desire to offload the defender in the January transfer window as he is no longer required at the Tottenham Hotspur Stadium.
The Independent has contacted Tottenham for comment.
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