The Netherlands international was stretchered off during the Swans' 1-0 defeat at Manchester City on Saturday and the club have since confirmed that he is set to be out of action for "six to eight weeks".
That leaves the route clear for deputy stopper Tremmel, who has only made four appearances for the club since his arrival in the summer of 2011, three of which have come in cup competitions.
"It will an interesting few weeks ahead," the backup keeper told the club's official website. "We have Liverpool on Wednesday [in the Capital One Cup] and Chelsea next Saturday.
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Tremmel added that, though his introduction from the bench at the Etihad Stadium was a baptism of fire, he felt that his team-mates acquitted themselves well at the home of the defending league champions.
"Luckily I didn't have much to do when I came on because the team played so well," the relieved German continued. "I think we deserved at least a point because in the second half, especially, we created some good chances.
"We dominated Manchester City in the second half and it's something we need to take positives from, particularly when you realise they only created one chance."