The Argentinian club have seen 20 players, including all of their eligible goalkeepers, test positive for COVID-19, leaving Marcelo Gallardo with just 10 fit members of his squad for the Group D game.
CONMEBOL ensured River will have to put an outfield player in goal after the governing body rejected a request from the club to add academy goalkeepers Alan Leonardo Diaz and Agustin Gomez to the squad.
Midfielder Enzo Perez, who has a hamstring injury, appears likely to play as River's stand-in goalkeeper following a decision that angered club president Rodolfo D'Onofrio.
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"We would never have thought that they could make a decision of this type," D'Onofrio told ESPN.
"We made a presentation where we perfectly clarified why we consider that the goalkeeper can be substituted at any time during the competition.
"There is an article [in the competition's regulations] that talks about serious injury. We consider COVID as a serious injury.
"We have 18 outfield players and three goalkeepers. We put the 32 players with four professional goalkeepers, who were infected. What we ask is to replace them."
Of River's available players, just six have started a top-flight game for the club, though the Colombians have their own coronavirus issues, with five Santa Fe players having tested positive ahead of the game.
River are second in Group D, level on six points with another Colombian club in Junior, who have played a game more. Santa Fe are bottom with two points from four games.
Argentina has the seventh most active cases of coronavirus in the world with over 307,000. Colombia is 19th with over 114,000 as the virus continues to ravage South America.