Benson was forced to leave Wednesday's game when he experienced discomfort in his right shoulder, and the club is calling his injury a shoulder strain.
"Hopefully it is nothing major and we can get him back in the mix for the rotation," D-backs manager A.J. Hinch said.
Rosales had been experiencing pain in his left foot since the team's series in San Diego, but had been attempting to pitch through it while having his foot wrapped. He has been diagnosed with a foot sprain.
Rosales had been pitching well before allowing seven runs in 1 1/3 innings Wednesday.
"He was getting better, but then he took a step back yesterday," Hinch said.
After finally getting a chance to pitch in the big leagues and have success, Rosales had been reluctant to go on the disabled list. When a reporter noticed he had his ankle wrapped earlier this week and asked him about it, he said, "I'm not coming out, I'm not going on the DL. No way. I just want to keep pitching."