Liriano threw 123 pitches and struck out only two batters while walking six.
The 27-year-old is the fifth pitcher from the Dominican Republic to throw a no-no. Juan Marichal, Ramon Martínez, José Jiménez and Ubaldo Jiménez also achieved the feat.
Liriano shared the award Justin Verlander, who also tossed a no-hitter last week.
In the National League, Gaby Sánchez won the award with a week that saw the Florida Marlins first baseman hit .464.
The Miami native had 13 hits, 10 RBIs and 22 total bases. He had a .531 on-base percentage, too.
The 27-year-old slugger, who is a Miami native of Cuban descent, hit his first career grand slam on Monday.