Justin Faulk, a 21-year-old who plays for the Carolina Hurricanes, will make his Olympic debut in Martin's place.
Martin practiced with the team on Thursday, according to ESPN.com's Scott Burnside.
But he was seen wearing a cast on his hand after the morning skate on Friday, according to Julie Stewart-Binks of Fox Sports. The NBCSN broadcast during the Finland-Sweden semifinal reported that Martin was ill, but Rob Rossi of the Pittsburgh Tribune-Review later said it was "definitely" a hand injury.
USA Hockey has not confirmed either report.
Martin has averaged 17:54 of ice time in Team USA's first four games (all victories), which is the third most on the team behind Ryan Suter and Ryan McDonagh, according to Sean Leahy of Yahoo Sports. Team USA has allowed six regulation goals in its four games.
Paul Martin definitely has hand injury, not illness. Will not play for #TeamUSA. No timetable for return to #pens — Rob Rossi (@RobRossi_Trib) February 21, 2014