The Dane, who scored Rangers' winner against Partick Thistle on Sunday, was left in agony following a late challenge from Ian Ross.
Replays showed the true horror of the incident, with Lovenkrands' left ankle twisting under the pressure of the challenge.
The Dane received lengthy treatment on the pitch before being stretchered away.
Lovenkrands received further treatment in the dressing room, with club doctors confident he had not suffered a broken ankle.
However, the amount of swelling meant a scan could not be performed straight away - giving McLeish an anxious wait.
''We are concerned about Peter but will have to wait 24 hours to see the full extent of the damage," said McLeish.
McLeish feels Ross was lucky to escape without censure, as he added: "I've seen the incident on television and it wasn't a great tackle.
''Michael Ball was booked earlier for what I think was a less serious tackle but the referee obviously hasn't seen it.
''Peter's ankle is definitely bent under the pressure of the tackle and if it is twisted then he will be a big doubt for the semi-final on Thursday.
''Thankfully both sets of players managed to get the referee to call a halt to proceedings because they knew Peter was in trouble.''
