A small makeshift clinic for carrying out the procedures was erected in Parliament House in the capital Harare.
Blessing Chebundo, chairman of Zimbabwe Parliamentarians Against Aids, said his main objective was to inspire other citizens to follow suit.
Research by the UN has suggested male circumcision can reduce the spread of HIV and Aids.
A report by UNAids and the World Health Organisation (WHO) said the risk of HIV infection among men could be reduced by 60%.
More than a million people in Zimbabwe are believed to be HIV-positive, with about 500,000 receiving anti-retroviral treatment.
The country was one of 13 African states identified in 2007 as a priority for the development of male circumcision programmes by the WHO and UNAids.
Mr Chebundo said more than 120 MPs and parliamentary staff had shown an interest in the circumcision programme.
The BBC's Brian Hungwe, in Harare says at least 10 MPs and 13 other people had the procedure performed.
Blessing Chebundo was the first to undergo the 10-minute operation.
He told the BBC there was a possibility that some members of the executive may also attend, including President Robert Mugabe.
The circumcision programme had attracted a lot of attention in Zimbabwe, and had divided opinion, our correspondent said.
The issue was raised in parliament in September 2011, when Deputy Prime Minister Thokozani Khupe made a plea to her fellow politicians.
At the time, many MPs shunned the idea. As well as a clinic in parliament, the initiative has seen a tent set up across the road from parliament, where counselling sessions will be held.