The Athletic's David Ornstein stressed the positive point that neither player requires surgery and both will recover in time for pre-season.
Centre-back Saliba was injured in the second leg of the Europa League clash with Sporting, a significant absence that contributed to Arsenal's dismal April form of no wins in four games - a run which saw the Gunners concede their league lead to Manchester City.
Zinchenko, meanwhile, was substituted with a calf problem in Arsenal's game against Newcastle on Saturday, which ended in a 2-0 win for the north London side.
On Sunday, Arsenal face Brighton after City's tie with Everton in an attempt to return to the top of the table. The Gunners currently have one point less than their rivals having played one game more than Pep Guardiola's side.
