Grande, whose single "Problems" has sold 2.3 million tracks, co-starred on the series with another longtime Nickelodeon personality, Jennette McCurdy.
"We are very proud of the show and its very talented cast, and we wish them all the best," Nickelodeon said.
It's unusual for a network to end a highly rated series so quickly. After an initial order of 20 episodes, Nick doubled it to 40. But the series shut down production this spring, four episodes short of a full order amid published reports of turmoil on the set and a falling out between Grande and McCurdy.
Representatives for the actresses did not immediately return messages seeking comment.
Nickelodeon would not comment on why production was cut short. Its executives said that both stars had reached 21 and were anxious to move on in their careers.
While Grande's musical career was taking off, some racy pictures of McCurdy surfaced online.
The creator of "Sam & Cat," Dan Schneider, is making a new series for Nick, titled "Henry Danger." It's scheduled to premiere in the fall.