The trooper is reportedly part of a counterterrorism drive in Iraq and Syria, which has been operating since the beginning of the year.
A source told the newspaper that the village in question was under Isis control making a more preferable "capture mission" impossible. The exact location has not been revealed.
"The SAS team had hoped that the Isis commander would arrive during the day because a night shot was regarded as too dangerous," the source said.
"But as evening approached the team realised that they were going to have to either abort or go for a night shot. The sniper said he wanted to take the shot and was given a 'go order'."
The sniper had 15 seconds to take his shot as the extremist pulled up in a car. The source said the extremist was killed instantly after being shot in the back of the head.
The Ministry of Defence declined to comment when contacted by MailOnline this morning.