Less than two days before the game, Chiellini suffered the problem in his side's last training session before travelling to Amsterdam for the first leg.
The result is that Chiellini is seen as doubtful for Wednesday's clash as the club may very well have to play without the veteran central defender.
Chiellini has started 21 Serie A matches for the club while also making six further appearances for Juventus in the Champions League this season.
Daniele Rugani is the most likely replacement for the Italy international as both Martin Caceres and Andrea Barzagli are currently dealing with injury issues of their own.
Emre Can and Douglas Costa are also seen as doubtful for the Serie A leaders while Cristiano Ronaldo could make his return to action having missed the last three matches through injury.
The Serie A leaders currently maintain a 20-point advantage at the top of the table and are just one point away from clinching another league title, the club's eighth in a row.
Following the first leg of the Ajax tie, Juventus will return to Serie A against SPAL on Saturday before playing host to the Dutch side in the second leg of their Champions League encounter with a semi-final berth on the line.