P Jared O'Mara has been arrested on suspicion of fraud, according to multiple sources.
The independent MP for Sheffield Hallam was arrested at the same time as his chief of staff Gareth Arnold, the BBC's Next Episode Podcast found.
Electronic equipment was confiscated in the South Yorkshire Police inquiry, the BBC also understands.
Mr O'Mara did not respond to requests for comment while Mr Arnold said he had "no comment".
Both have been released under investigation.
South Yorkshire Police would not confirm details of either man's arrest.
The Independent Parliamentary Standards Authority said it was a "matter for the police".
Mr O'Mara said he was "taking time out for mental health treatment" in July and promised to resign at the end of summer recess after allegations of sexual misconduct towards staff.
Constituents have complained that case work has not been dealt with in the MP's absence, allegations Mr Arnold denies.
Responding to the latest news, Sinead Parkinson, a member of the Hallam Constituents Facebook group, told the BBC: "We are pleased that an investigation is under way but we are still a constituency unrepresented and action needs to be taken to correct that."
During its investigation, the BBC uncovered staff running the MP's office without the proper security clearance required by Parliamentary authorities.
After the investigation was published, the constituency office was closed and staff formally given four weeks' notice.
The Treasury confirmed Mr O'Mara had, in recent weeks, given formal notice of his intent to resign in September.
When the BBC has visited the constituency offices, on a number of occasions, they were found to be empty.