O'Shea won five Premier League titles with United and earned 118 caps for Ireland.
"It will be an incredible honour to lead the side into the March international window," O'Shea said in a statement.
"As everyone will know, I've always had immense pride representing my country, whether that be during my playing career or very recently, as part of the coaching staff for the men's senior team and the Under-21s.
"I've got great belief in this group of players to win football matches and looking forward to some positive results."
The FAI said they would announce a permanent head coach in April. Stephen Kenny left his role as Ireland's head coach in November following the failure to qualify for Euro 2024.
O'Shea will be assisted during the international window by Crystal Palace assistant manager Paddy McCarthy.
