Feltner was injured Saturday night and was discharged from Swedish Medical Center on Sunday. He will not need surgery.
"Overall, he's fine," Colorado manager Bud Black said before Sunday's game. "I think the feeling is that it could have been worse."
Feltner, 26, was put on the 15-day injured list. When asked whether the right-hander will be out for days, weeks or months, Black said "probably on the longer end of that."
Feltner was hurt in the second inning when Castellanos hit a slider 92.7 mph back at the mound. The ball hit Feltner on the back right side of his head, and he fell to the ground. He lay on his stomach as two members of the Rockies athletic training staff aided. He was able to get on his feet and walked off the field with the assistance of the two trainers.
Black said Feltner was "still fairly lucid" and was texting with his teammates, his parents, team medical staff and the manager Saturday. Black said he thinks Feltner will be back with the team Monday or Tuesday.
"He just needs time to let the fractures heal and the concussion to diminish," Black said. "From everything that I've been told here this morning, things are looking up."
Feltner is 2-3 with a 5.86 ERA.
Right-hander Riley Pint was recalled from Triple-A Albuquerque, where the 25-year-old reliever has a 7.41 ERA in 13 appearances this season.
"At some point, we're going to need a starter for Ryan's spot," Black said. "We'll go through that process this week."
On Sunday, Colorado first baseman C.J. Cron left in the third inning of the Rockies' 4-0 victory over the Phillies with back spasms after he was tended to by athletic trainers along the first-base line following an inning-ending popup. He was replaced by Mike Moustakas.
"C.J. looks like he's probably heading to the injured list," Black said after the series finale.
The Associated Press contributed to this report.