Cristina Fernández de Kirchner was due to meet Pope Francis along with her Chilean counterpart to mark 30 years since a peace treaty was agreed between the two South American countries.
She and Michelle Bachelet had been invited to Rome by the Pontiff as a sign of better relations between them both.
"All activities programmed for the month of January are suspended, including the trip to the Vatican," Cabinet Chief Jorge Capitanich said.
Ms Fernández fractured her left ankle on Friday after slipping at home on a wet floor.
In the late 1970s Argentina and Chile almost went to war over a small cluster of islands but the dispute was resolved with the help of the Vatican.