Aaron Connolly and Callum Robinson will both miss all three of Ireland's upcoming games.
Ireland play England in a friendly on Thursday at Wembley and then Wales and Bulgaria in the Nations League.
Connolly picked up an injury during an Ireland training session on Tuesday. Robinson has been named as the positive Covid-19 case which the FAI confirmed on Tuesday evening.
Sean Maguire has been called up as a replacement for Connolly. Ryan Manning will also link up with the Ireland squad ahead of Sunday's game away to Wales.
Ireland's final game of the international window, against Bulgaria, takes place next Wednesday in Dublin.
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