The 49ers might have dodged disaster at tight end.

Vernon Davis and Vance McDonald both went down with injuries in Sunday night’s 28-20 loss to the Bears. Davis injured his left ankle in the fourth quarter, when his foot became tangled underneath Chicago linebacker Jonathan Bostic, and McDonald hurt his right knee on Frank Gore’s second-quarter touchdown run (which was negated by a penalty).

The 49ers did not offer any official updates today, but Davis’ MRI exam on Monday revealed a deep bruise and no structural damage, according to csnbayarea.com. The report suggested Davis could return for this Sunday’s game against NFC West rival Arizona.

McDonald said an exam of his knee showed no structural damage. He’s hopeful of playing against the Cardinals, saying, “There’s a chance.”

“I’m a little banged up, but the structure of the knee is perfectly fine,” McDonald said. “It’s a day-by-day thing.”

Asked if he could replace Davis if necessary, McDonald replied, “I don’t think anyone can be Vernon except Vernon.”

The injuries to Davis and McDonald leave Derek Carrier as the only healthy tight end on the 53-man roster. The 49ers did sign former USC tight end Xavier Grimble to the practice squad on Monday.

The 49ers must recover quickly as they prepare for this week’s trip to the desert. The Cardinals are 2-0, with wins over the Chargers and Giants. So the 49ers would tumble two games off the NFC West pace if they fall in Arizona.

It’s obviously early in the season, but at least one player acknowledged a sense of urgency.

“We lost one NFC game last week, and we definitely can’t afford to lose another,” defensive tackle Tony Jerod-Eddie said. “We’ve got to get this one.”