The goalkeeper picked up an injury in the win over West Bromwich Albion.
That run is set to end this weekend though as he will be forced to sit out the game against the Swans.
He reportedly picked up a hamstring injury in the win over West Bromwich Albion, although Bilic has insisted it is only a minor problem for his number one.
“We've got one player injured and that's Adrian,” he told the club's Twitter account.
“He felt his calf in the WBA game and it's a minor injury so he's out tomorrow. We've got a great deputy in Randolph. He's one of the biggest reasons we went far in the FA Cup and we are happy to have him."
The news will come as something of a blow for West Ham as they try to hunt down a top four place this season.
The Hammers are currently sixth in the table and five points behind Manchester City in fourth, but have a crucial game in hand against Manchester United.
To catch City they will need to win all of their remaining games, and equally need all of their first team stars fighting fit to do so.
That makes he loss of Adrian a blow for them, and they will be hoping Randolph can step in and fill his boots adequately.