Partick Thistle will host Rangers for their Scottish Cup quarter-final replay on Sunday 13 April.
The date had been put aside for the second semi-final, which will now be played at Hampden on Sunday 20 April.
St Johnstone await the winners of the replay and BBC Scotland have announced plans to broadcast the match live.
"We are delighted we have found the best solution available in the circumstances," said Scottish FA chief executive Gordon Smith.
Aberdeen meet Queen of the South in the other semi-final on 12 April, with the Hampden tie scheduled for a 1215 BST kick-off.
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