The England and Wales Cricket Board is now reviewing its security arrangements, including looking at whether members of the public who are banned from one ground can be barred from all venues, mirroring football.
"Any pitch invasion is completely unacceptable," an ECB spokesperson said. "The ECB and our host venues do not tolerate any such behaviour which risks the safety of players, officials and staff."
The invader was booed by the crowd after leading to an interruption in the play. Players were visibly angry that he had managed to get onto the outfield, with Bairstow appearing to be furious.
Virat Kohli, the India captain, also had discussions with the umpires after the security breach, which was the third in consecutive Test matches.
In the second Test, at Lord's, Jarvis entered the outfield posing as an Indian fielder.
In the third Test, at Headingley, he entered the outfield dressed as an Indian fielder – wearing full kit, including a helmet.
On both occasions the invader was thrown out of the ground, yet was still able to enter the Oval.
"I don't know how he's got on the pitch again, to be honest," said Ollie Pope, who was batting with Bairstow when the invader entered the field. "I just try to stay in my bubble and don't let it affect me.
"We don't really talk about it. I guess it just stops the play for five minutes every time he comes on. There's nothing to be gained from it.
"I think you just have to try to block it out and as a batter that's the art of batting: switching on and off. I try to switch off a little bit between balls but as soon as I'm there in my stance whatever has happened before, whatever happens in between the balls, I just tried to get a good place for that next ball. I try to avoid it. Obviously it does disrupt you for five minutes or so, so just try to block it out."