The Mets placed deGrom on family emergency leave Saturday because of health "complications" with Jaxon Anthony, who was born Monday night.
"Last night I talked to him," Collins said Sunday morning. "The baby is doing better. That was a good sign. I just told Jake he needs to get some rest and mix in a meal."
Collins said deGrom appears exhausted, "mentally more than physically."
The deGroms hope to take Jaxon home from the hospital on Monday, according to Collins.
DeGrom will be inactive for three to seven days, but he is continuing to throw off a mound during his absence from the team. He threw a 40-pitch bullpen session Sunday morning at the team's Florida complex after commuting 2½ hours from his family's home in DeLand. DeGrom next is due to throw a simulated game on Tuesday.
Team officials believe deGrom could re-enter the rotation for an abbreviated outing as soon as next weekend in Atlanta if his family situation allows.
"I've spoken to him every day," Collins said Saturday. "He's where you would expect him to be. He's not sleeping much. We're certainly rooting for him and [his wife] Stacey and the baby to hang in there. ... It's a real-life situation. Certainly we take the game of baseball very seriously. This changes a lot of things."
DeGrom had been scratched from his start last week against the Miami Marlins because of right lat tightness, before the baby was born. Had his family issue not arisen, deGrom likely would have been capable of taking his next turn on Tuesday in Philadelphia.
Utility player Eric Campbell has returned from Triple-A Las Vegas to take deGrom's roster spot. That restores the Mets to a standard five-man bench.
DeGrom allowed one run on five hits in six innings against the Phillies on April 8 in his lone appearance so far this season, but his fastball velocity sat at 92.4 mph. That is 2.5 mph off his fastball velocity average in April 2015.
The Mets have suggested that deGrom's fastball velocity is not the result of injury but instead likely reflects a hangover from last year's heavy usage, which they hope he eventually will shake. DeGrom tossed 216 innings, including the postseason, in 2015.