Left-armer Panesar, 25, claimed his first 10-wicket haul in Tests when England took an unassailable 2-0 lead against West Indies in the four-match series at Old Trafford on Monday.
- Schedule: West Indies in England
During one spell, Pakistani umpire Aleem Dar politely asked him to appeal before celebrating, but did not take the matter further.
"We're in a position of maybe taking characters out of the game," Vaughan told reporters on the eve of the final Test at Chester-le-Street.
"We all love Monty Panesar, he appeals, he celebrates with a high-five, he's brilliant for the game. We don't want to see that taken away.
"If it gets too much and he's appealing every ball, yes we may say something but at the minute he's a young lad having fun, bowling brilliantly and entertaining a lot of people. Let him continue. He's an excitable character and good for the game."
With his signature beard, black turban and clumsy fielding, Panesar has been a standout figure with English crowds.
Panesar, the first Sikh to play for England who was born in Luton near London, claimed his 50th Test victim at Old Trafford.
"It's a lot better having someone who appeals too much than someone who doesn't appeal at all because you know he's creating chances," Vaughan added.
"I'm not knocking him down and the team aren't knocking him down. We just want to see him continue having fun and showing the same control and expertise. If he thinks the decision is 'out' he is going to appeal."
Matthew Hoggard is set to return to the team in place of Liam Plunkett after missing the last two Tests with injury.
West Indies stand-in captain Daren Ganga urged his team to maintain self-belief despite not winning any of their last 19 Tests.
"It's very difficult for young players coming into a team that is not winning and having to put in a big effort time and time again and getting nothing at the end of it," Ganga said.
"We all have to ensure we have the right work ethic and believe strongly that we are going to win and we are going to get back to our winning ways."
