The Poland keeper had only just returned to the side following fitness problems, ousting countrymen Wojciech Szczesny as he delivered a clean sheet in the Champions League away win over Bayern Munich and then also at Swansea.
However, Fabianski missed the midweek goalless draw against Everton at the Emirates Stadium, and is now set to be monitored "day by day" to assess his availability for the crucial run-in as Arsenal looks to cement a top-four finish.
"Fabianski has a crack in his rib that has not moved, so we have to treat it clinically," said Wenger, whose side travels to Fulham on Saturday.
Szczesny, who turned 23 Thursday, coincidentally sharing a birthday with his Polish teammate, had little to do against Everton, but was alert enough when called up.
Wenger was happy with the goalkeeper's response to being dropped -- which had brought stinging public criticism from the player's father.
"He had a good performance, I was pleased with his focus, with his sharpness," the Arsenal boss said.
"He dealt well with the situation that he faced. In our job there is only one way to respond, to practice harder and stronger and show that you are ready for a fight, that is what he did."