Likely topics for discussion include the North American Free Trade Agreement, which Obama has said he would like to renegotiate, immigration and the drug trade.
The two leaders are having their private talks over lunch at the Mexican Cultural Institute in Washington before a brief photo opportunity in front of the media. Obama transition officials say the meeting is intended to underscore the importance of the relationship between Mexico and the U.S.
New U.S. presidents traditionally meet with their Mexican counterparts either before they are inaugurated or shortly afterward.
Calderon is scheduled to sit down with President George W. Bush on Tuesday.