Nick Eatman of the Cowboys' official website noted Elliott suffered a head injury in the accident. Slater pointed out Elliott did some work on the side as a "precaution" while his teammates took part in OTAs.
Adam Schefter and Todd Archer of ESPN confirmed Wednesday the running back has missed the last two days of offseason practices. Schefter added Elliott "did not suffer any significant injuries" in the crash, but the Cowboys have decided to play it safe with him.
Head coach Jason Garrett said the team learned of Elliott's accident on Monday, and he will be held out until practice on May 30, per Jane Slater of NFL Network.
The running back was previously involved in a January collision near Dallas' practice facility. A.J. Perez of USA Today passed along comments he made about that incident.
"Just got into a little accident, glad that no one is injured," Elliott said. "That's all I'm going to talk about it."
Further information about Sunday's accident wasn't made immediately available.
Elliott was a dominant force for the Cowboys last season as a rookie. He led the NFL with 1,631 rushing yards on 322 carries to go along with 15 touchdowns. He added 32 catches for 363 yards and one score as part of the passing game.