Members of the opposition left-wing Democratic Revolution Party tried to block the podium where Calderon was set to take the oath of office. The president's opponents traded blows with his supporters before Calderon was eventually sworn in.
The protesting lawmakers contend that the election earlier this year was a fraud.
Calderon defeated Andres Manuel Lopez Obrador by less than 1 percent, exit polls showed.
Earlier this month, Obrador declared himself the alternative president of a parallel government following his own inauguration ceremony.