Young said he initially injured the thumb while catching a ball awkwardly, and he aggravated it when he took an awkward swing while striking out in the eighth inning on Monday night.
"I tweaked something in there, and [on Tuesday] when I woke up, it was a little stiff," Young said. "I'm just going to try and get some work done on it, and get it better."
D-backs manager Kirk Gibson offered to give Young a day off, but he declined.
"It felt a lot better [on Wednesday] when I woke up than [on Tuesday], so I'm assuming it should be fine," Young said. "It was initially more [painful] catching. Swinging, I don't really use that thumb much when I swing. It's more on a bad swing and miss or when I roll over a pitch that I feel it. It's not too bad. It's going to be fine."