UFC officials announced the news on Friday, but no further details about the nature of the injury were provided.
Koscheck (17-7) has lost back-to-back fights and was looking to rebound against Maia on the August 3 fight card.
Maia (18-4) was looking to extend his winning streak to four consecutive fights. Since dropping down from the middleweight division, Maia has won three fights in a row as a welterweight with wins over Dong Hyun Kim, Rick Story and Jon Fitch.
Maia has been removed from the card, and it is unknown how long Koscheck will be sidelined.
UFC 163 takes place at HSBC Arena in Rio De Janeiro, Brazil. The main card airs live on pay-per-view with preliminary action airing live on FX and streaming live on Facebook.