Senzel came out of the game against the Rangers on Saturday night and got three stitches, manager David Bell said after the Reds' 4-3 loss.
Bell said before the Reds' 11-3 victory Sunday that Senzel was available off the bench, but he was not used in the game.
The outfielder fouled a pitch from Mike Minor into the dirt, the ball deflecting off his foot and hitting the bill of his helmet and his eye. A trainer applied a towel and helped Senzel off the field.
The ball hit Senzel above the eye, Bell said.
"He's fine. He had a few stitches. His eye is fine. ... Nothing serious -- fortunately, he closed his eye in time," Bell told reporters.
Jesse Winker played center field in Senzel's place on Sunday and went 4-for-5 with a home run and five RBIs from the leadoff spot.
Senzel was the second overall pick in the 2016 Major League Baseball draft out of Tennessee, getting a $6.2 million bonus. Bouts of vertigo and a broken right index finger slowed has ascent. He sprained his right ankle during spring training and made his debut on May 3.
Senzel hit three homers in his first four games, a franchise record. He is currently hitting .266 with six home runs and 16 RBIs.
The Associated Press contributed to this report.