Wayne Bvudzijena, police spokesman, said that he was unaware of Monday's arrests, and added "it would be illegal for anyone to be arrested while they were proceeding to parliament".
The ruling Zanu-PF party of Robert Mugabe, the president, suffered a historic reverse in the elections in March, winning only 97 seats compared to 100 taken by the MDC. A splinter party formed and led by Arthur Mutambara, a former MDC politician, has 10 seats.
MPs were sworn in in groups of 10, with some of the 210 politicians having to stand as there was only seating for 145 people.
MDC members sat on the side usually occupied by Zanu-PF, heckling members of the party by shouting: "You sit on that side. You are now in the opposition."
The MDC has nominated Lovemore Moyo, the party's national chairman, as speaker, while Mutambara has put forward senior party member Paul Themba Nyathi for the same position, MDC officials said.
Despite holding only a small number of seats, Mutambara's camp holds a pivotal position as both Zanu-PF and the main MDC faction are unlikely to be able to win a vote on the speaker without his help.
"Zanu-PF will probably side with the Arthur Mutumbara faction, that is what I am hearing from a member of parliament this morning," Al Jazeera's Haru Mutasa, reporting from Harare, said.
"That would mean that Morgan Tsvangirai's faction would get the deputy seat, that's not what they want."
Earlier Chamisa said: "We hear that they are also looking for a total of 15 of our members of parliament as part of an evil ploy to rig the elections for parliamentary speaker."
The police also apparently attempted to arrest Elton Mangoma, one of the representatives of the MDC at recent power-sharing negotiations with the governing Zanu-PF of Robert Mugabe, the president.
Other MDC politicians prevented Mangoma from being taken away, sources told Al Jazeera.
Chamisa said that the MDC would not allow the vote for the speaker of the house to go ahead after the arrests.
"Clearly they have chosen the path of arrogance, unilaterilism, that is a serious blow to confidence building in the talks," Chamisa said.
Representatives of Morgan Tsvangirai, the MDC leader, and Mugabe have been locked in power-sharing talks aimed at resolving the long-running dispute created by Mugabe being sworn as president after Tsvangirai pulled out of a presidential run-off vote.