The Manchester United midfielder picked up the problem in training on Wednesday and was sent for a scan to establish the extent of the damage.
Fellaini scored twice in Belgium’s 4-3 win over France on Sunday but Belgium coach Marc Wilmots has confirmed the player won’t be considered for selection in Cardiff.
Manchester City defender Jason Denayer, who spent last season on loan at Celtic, also left the training session early.
Belgium, who are second in the FIFA world rankings, have plenty of depth to their squad but the loss of Fellaini would still come as a huge blow to the Red Devils.
The powerful 27-year-old has scored eight goals in his last 13 games for club and country.
Belgium lead the way in Group B at the halfway stage of the European Championship qualifying but only on goal difference with Wales in second place.
Watch Wales v Belgium, live on Sky Sports 5 HD from 7pm on Friday.