The team announced the moves in a statement Tuesday.
DiPietro sat out Saturday night's game against the Phoenix Coyotes because of swelling in his right knee. The former first-overall draft pick, who is 4-6-4 with a 3.68 goals-against average this season, is eligible to return after seven days.
Mottau will miss the rest of the season after surgery on his right hip.
He'd been out the past 10 games because of an eye injury, was cleared for physical activity last week, then tore the labrum in his right hip. The defenseman had three assists in 20 games.
The Islanders return to action Wednesday night against Tampa Bay.