Jaros, 24, suffered a severe ACL injury in training and will undergo surgery, ruling him out for the rest of the season.
The Czech stopper was Ajax's starting goalkeeper for the majority of the season after arriving on loan from Liverpool in the summer, making 26 appearances across all competitions and conceding 42 goals.
Indonesian international Maarten Paes is expected to take over as Ajax's number one. The 27-year-old arrived from MLS outfit FC Dallas in January.
Injury issues
Jaros' injury is the second severe injury Ajax have suffered in recent days, with former Arsenal left-back Oleksandr Zinchenko also ruled out for the rest of the season after suffering a knee injury in last weekend's 4-1 win over Fortuna Sittard.