Volquez and Ventura were teammates with the Kansas City Royals, helping the team capture the 2015 World Series title. Ventura died in a car crash in his native Dominican Republic in January.
"[Ventura] was one of my best friends. I'm pretty sure he's in the right place right now, enjoying this moment right now," Volquez told Fox Sports Florida after the Marlins' 3-0 win in Miami.
Earlier Saturday, Volquez posted on Instagram a picture of the two together while with the Royals. His no-hitter comes on the same day as what would have been Ventura's 26th birthday.
Volquez also dedicated his achievement to Fernandez, the late Marlins pitcher who died in a boat crash last September. Volquez was one of the pitchers the Marlins brought in this past offseason in part to fill the void caused by the death of Fernandez.
"They watching right now, what happened today. And they must feel really happy right now," Volquez said.
Volquez finished with 10 strikeouts and two walks. He struck out the side in the ninth inning.
Thee right-hander was nearly knocked out of the game after just one batter, when he collided with Diamondbacks leadoff man Rey Fuentes as he covered first, rolled his ankle and took a hard fall to the turf.
"I thought I broke my ankle,'' he said jokingly after the game.
The last no-hitter in Marlins history was thrown by Henderson Alvarez in 2013.
Volquez needed just 98 pitches to complete the feat. The Marlins now have thrown the most no-hitters in baseball (six) since entering the league in 1993.
The Associated Press contributed to this report.