Kubel left Friday's game against the Cubs with tightness in his hamstring. He was out of the lineup Saturday but came on to pinch-hit in the ninth, grounding into a game-ending double play.
While Kubel was left out of the lineup both Sunday and Monday, D-backs manager Kirk Gibson said the club considered pinch-hitting Kubel again Sunday.
"He was somewhat stiff [Sunday] before the game, so we'll try to avoid going backwards with this," Gibson said. "As much as you want to do things, sometimes you just couldn't do it."
Gibson called the injury "a little concerning" but added that they don't plan on putting the 30-year-old on the disabled list.
"He doesn't want to [go on the DL], we know that," Gibson said. "We don't want to put him there, but time will tell. If he doesn't get well in the next couple days, then we'll probably be more inclined to consider that."
Arizona could use Kubel's bat in the lineup after scoring just three runs in as many games in Chicago.
Kubel began the day batting .292 this season and led the team with 15 home runs and 60 RBIs.
"I'm feeling better," Kubel said. "Each day is better and I'm able to get looser easier."
With the team on a four-game visit in Cincinnati, Kubel believes his chances of making a recovery are higher than they were using the dated facilities at Wrigley Field in Chicago.
"I haven't really had many opportunities like we have [in Cincinnati]," Kubel said. "Chicago is a little different place. There's a lot more I can do here to get ready and prepare my body."
Kubel said he hopes to be back in the lineup Tuesday.