Rodriguez left Ameriquest Field on a stretcher and was taken to a hospital.
Commissioner Bud Selig issued Rogers a 20-day suspension and an undisclosed fine -- reported to be $50,000 -- on Friday.
But Rogers is appealing the suspension.
So he was able to make his Sunday start against the Mariners in Seattle and he will be allowed to join his teammates Mark Teixeira, Alfonso Soriano and Michael Young at the Midsummer Classic at Detroit's Comerica Park on Tuesday, July 12.
"He was voted on the team by the players and the league, he appealed his suspension, the league is not going to look at that until after the All-Star Game," said Red Sox manager Terry Francona, who will manage the American League team in Detroit. "So I abide, like everybody else, by the league rules. That's kind of where it starts and it ends."
On the season, Rogers is 9-4 with a 2.45 ERA.
"Kenny, the last two years, he's probably had as good of years he's had in his career," Rangers manager Buck Showalter said. "I'm real proud to have a front row seat and watch it. I'm real proud of all our guys. The fans did a good job and, I thought, the players, the coaches and managers did a good job. It's a system that seems to be working a lot better."
Rogers has yet to make a public statement about Wednesday's incident. His lawyers, Tim Evans and Mark G. Daniels, issued the following statement on Friday:
"Kenny Rogers would like to make a statement. However, in light of the ongoing investigation, it is not advisable for Kenny to comment directly and publicly at this time.
"On Kenny's behalf, though, we would like to express to Mr. Rodriguez, Rangers fans, all baseball fans and his teammates that Kenny is truly sorry for the incident that occurred and regrets that it happened."
Angels manager Mike Scioscia said the incident shouldn't take away from what Rogers has done on the mound during the first half of this season.
"What Kenny did was wrong. I think everybody knows that and he's going to pay a price for it," Scioscia said. "But do you negate everything he has done in the first half as far as being an All-Star pitcher? That's a tough question. He's going to pay a price, but I don't think it lessens the impact of what he did in terms of pitching performance."
On Sunday, Rogers was charged with two runs on six hits and picked up the loss. The start was his first since allowing 10 hits and six runs in 3 1/3 innings against Anaheim on June 22, also a loss. He missed his next scheduled start while recovering from a broken bone he sustained in his non-throwing hand after punching a cooler following an outing against Washington on June 17.
"We expected Kenny to pitch well today," Young said. "As far as we're concerned, when the game starts, all that stuff is over. Those three, three and a half hours on the field, that's our time to put it all aside and go play baseball. I'm sure Kenny feels the same way. We expected him to go out and pitch like Kenny does and he did. It's a shame we couldn't help him out a bit."