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 and is now set to be monitored "day-by-day" to assess his availability for the crucial run-in as Arsenal look 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 travel to Fulham on Saturday.
"That means has he pain or does he not? That is day by day."
Szczesny 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."
Wenger felt referee Neil Swarbrick should have taken a firmer stance against what was some tough tackling by Everton on Tuesday night, when midfielder Darron Gibson stayed on the pitch despite twice pole-axing Theo Walcott.
The physical approach of some players was again highlighted in yesterday's Premier League game between Manchester United and West Ham at Upton Park, where Irons striker Andy Carroll clattered into goalkeeper David De Gea in a challenge which Red Devils boss Sir Alex Ferguson claimed should have resulted in a red card.
Wenger admitted he could see both sides, adding: "He went for the ball at the start, but he was too late."