Thakur, in her late 60s, was arrested from her house in Sector 31 on Friday.
She is accused of extortion, forgery and criminal conspiracy linked to a pre-election 'sting operation' done by a gang helmed by a man who ran a local news channel that was shut down after demonetisation.
According to Noida's Senior Superintendent of Police Vaibhav Krishna, the gang was demanding Rs 2 crore from the minister after threatening to make public an "objectionable" video.
Three persons directly linked to the case have already been arrested in April.
Sector 20 SHO Rajvir Singh Chauhan said that Thakur was arrested following detailed interrogation of other accused involved in this case.
"She had facilitated the meeting between the people who conducted the so-called 'sting operation' and the Union Minister. She has been arrested based on evidence of her role in the whole conspiracy," he said.
Thakur was produced before a local court, which sent her to judicial custody.
Earlier in April, police had arrested Alok Kumar, the owner of the now defunct news channel, from Kolkata along with his aide Nisha.
Another accused, identified as Khalid, who worked in the gang and is named in the FIR, is absconding, the SHO added.
Interestingly, Ajay Sharma, the brother of the minister who had lodged the complaint in the matter, said that he had not named Usha Thakur in the complaint. Mahesh Sharma is known to have addressed her as an 'elder sister' on several occasions.