Rodriguez will make his first start since May on Sunday against the Los Angeles Angels.
The 29-year-old did not divulge the full reason behind his absence to reporters. He did address his teammates privately, and said they gave him their full support.
"(My teammates) are really the ones who have to know what really happened in my life, because I'm here with them every day, and I just want to keep it the way it is, keep it with them and with my family back in Miami," Rodriguez said, according to The Athletic's Cody Stavenhagen.
"It was difficult to step away from my career, my teammates, and everything, but for me, family is always first. My second family is my teammates and the organization," he added, per MLive's Evan Woodberry. "They've given me an opportunity to be here, and I'm back with my second family."
Rodriguez joined Detroit on a five-year, $77-million contract in the offseason and was the team's Opening Day starter. However, he posted a 4.38 ERA and 1.33 WHIP over just eight starts to begin the year before landing on the injured list with a ribcage sprain on May 22.
Three weeks later, the team moved Rodriguez to the restricted list due to a personal issue. It was unclear whether he would return to the club, and the Tigers were unable to reach him for some time.
Rodriguez finally returned in late July, beginning with a throwing program at team facilities before making three minor-league rehab starts this month. In his most recent rehab outing at Triple-A Toledo on Tuesday, he allowed one run while striking out 11 - three of which came in an immaculate inning - over six innings of work.
The Valencia, Venezuela, native owns a lifetime 65-42 record with a 4.17 ERA, 3.84 FIP, and 926 strikeouts across parts of seven major-league seasons. Rodriguez also helped the Boston Red Sox win a World Series title in 2018.