Hunter was placed on the 15-day disabled list Friday with a strained right side.
He has been playing hurt since crashing into the wall at Dodger Stadium on May 24, a 10-7 win over the Los Angeles Dodgers.
He underwent an MRI exam on Wednesday.
"I didn't want to go on the DL -- that's not me -- but maybe it's for the best," Hunter said on the Los Angeles Web site Friday.
Cruz, the next-highest vote getter among his major league peers, became the 27th first-time All-Star among the 66 players to play in Tuesday's game at Busch Stadium.
He is batting .262 with 20 homers and 50 RBI.
Hunter is batting .305 with 17 homers with 65 RBI.
Celebrity Families of 2014 [PHOTOS]