Senior Left leaders Brinda Karat and Subhasini Ali, on Thursday met the family members of the woman and then the Special Investigating Team (SIT) members.
Talking to reporters, the two leaders said that action had been taken against the victim under apparent pressure from the ruling BJP.
"The woman could have been given bail but she is being intimidated. We have given a memorandum to the SIT asking them to act in an impartial manner. It is clear that the 'victim' woman has been implicated in the case by the UP police on the directive of some senior politic of the state," said Karat.
Karat and Subhasini Ali also went to the Shahjahanpur jail to meet the woman.
Samajwadi Party president Akhilesh Yadav also attacked the state government over the arrest of the law student in the extortion case involving Chinmayanand.
In a tweet on Thursday, Yadav said that the BJP had shown their 'true face' by arresting the student who spoke against its leader.
"Today, all the daughters, sisters and mothers of the country are unhappy with BJP, but some people are saying 'All is well' in country. This is shameful," he said.
He alleged that the party's slogan of 'Beti Bachao' has proved to be just another 'jumla'.
The Shahjahanpur girl was sent to judicial custody for 14 days on Wednesday morning after she was arrested by a Special Investigation Team (SIT) in the extortion case involving the former union minister.
The SIT had earlier booked three of the law student's friends after questioning them in connection with a video clip in which they were purportedly discussing extortion.
According to SIT chief Naveen Arora, the three had accepted their involvement in the extortion case, although the law student had denied the charges.
Arora said during the interrogation, the three youths have claimed that the 'victim' girl was the main conspirator in the extortion case.
( With inputs from IANS )