Miley struck out eight on 114 pitches, issuing one walk and having another baserunner reach on an error.
This marked the first time that catcher Tucker Barnhart was behind the plate for a no-hitter.
"(It's) far and away the coolest thing I've done in my career," Barnhart said, according to Bobby Nightengale of the Cincinnati Enquirer.
This achievement marks the third complete game of the 34-year-old Miley's career and first since throwing a five-hit shutout against the Kansas City Royals in 2016.
Homer Bailey was the last Reds pitcher to throw a no-hitter, accomplishing the feat twice - once in 2012 and again in 2013.
Cleveland starter Zach Plesac similarly held Reds hitters in check through eight scoreless innings before Cincinnati managed to scrape across three runs against closer Emmanuel Clase in the ninth. Clase hadn't allowed a run through 14 1/3 innings entering the night.
This is the second time this year the Indians have been no-hit, with Chicago White Sox pitcher Carlos Rodon being the last to hold Cleveland out of the hit column on April 15.
The two-day gap represents the shortest span between no-hitters since June 29, 1990, when Oakland Athletics right-hander Dave Stewart and Los Angeles Dodgers lefty Fernando Valenzuela each accomplished the feat on the same day.
The last time the league saw four or more no-hitters by May 7 was in 1917 when there were five, and only one more was thrown by the end of that campaign.