The injury happened when Tannehill took a low hit from Cardinals defensive lineman Calais Campbell. Tannehill was injured on.
Asked for specifics of the injury, Gase simply said, "It doesn't look good". We've just got to get the final results.
Backup quarterback Matt Moore replaced Tannehill in the fourth quarter and would likely fill in for him for the remainder of the season.
The Cardinals closed their deficit to 21-15 on a 9-yard touchdown pass from Carson Palmer to Brittan Golden in the left corner of the end zone.
Tannehill's demeanor and interactions with teammates after he returned to the sideline in street clothes suggest that the preliminary news isn't good.
Tannehill was on crutches in the locker room and didn't talk to reporters after the game.
Miami would surprisingly score its second touchdown four minutes into the second quarter following an Arizona punt, but back to script, the Cardinals needed just three plays for Palmer to fumble it back to the Dolphins. The Dolphins overcame 14 penalties for 118 yards, and Arizona had seven for 54.
U.S. life expectancy shortens for first time in decades
The figures show rises in several causes of death, especially heart disease, dementia and accidental infant deaths. The latest numbers technically mean that someone born in 2015 is expected to live an average of 78.8 years.
Arizona running back David Johnson exceeded 100 yards from scrimmage for the 13th consecutive game this season, tying an National Football League record set in 2005 by Edgerrin James.
Together, that combination of factors made for quite a back-and-forth between the Cardinals and Dolphins on a rainy Sunday afternoon in Miami.
On the ensuing drive, Arizona scored on a 56-yard end-around by wide receiver J.J. Nelson, who made a decisive cut and was not touched.
Turnovers are a big reason for the Cardinals' disappointing season, and they helped the Dolphins start their first six possessions at their 48, the Arizona 35, their 37, the Arizona 10, the Arizona 43 and the Arizona 39.
Catanzaro missed a 41-yard field-goal try when he hit the right upright, and swung an extra-point wide to the left.
Tannehill lost the handle on a screen pass and the ball skittered backward for a 21-yard loss before rolling out of bounds. The good news on that front: Denver, ahead of Miami in the wild-card race, also lost Sunday.