The Thomson Airways jet with 189 people aboard took off from London and was headed to the Red Sea resort, according to The Guardian.
It said the jet came within 1,000 feet of a missile in its trajectory August 23, and went on to land safely. The paper said passengers were kept in the dark about the incident.
The revelation comes days after a Russian passenger jet crashed in the Sinai Peninsula last weekend, killing all 224 people aboard. U.S. and UK officials have said there may have been a bomb aboard the jet.
A UK government spokesman confirmed the media reports, but he did not provide any specifics.
"We investigated the reported incident at the time and concluded that it was not a targeted attack and was likely to be connected to routine exercises being conducted by the Egyptian military in the area at the time," the spokesman said in a statement.
An Egyptian official said Saturday that the incident involved a ground to ground military fire exercise at a military base a few kilometers from the Sharm el-Sheikh airport and that the plane was in no danger.
"No ground-to-air firing was involved whatsoever," Egyptian foreign ministry spokesman Ahmed Abu Zei said via Twitter, adding that airliners were informed about the military exercise.
In a statement, Thomson Airways said "an event was reported by the crew of flight TOM 476" on August 23. The statement did not describe the event, but said an investigation "concluded there was no cause for concern" and it was safe to fly into Sharm el-Sheikh.
The British Airline Pilots Association (BALPA) said in a statement that "the safety of the aircraft was not put a risk" and described the incident as "separate from the current and ongoing security situation in Sharm el-Sheikh."
Thomson Airways said in a statement that UK Department of Transportation determined the incident was "a routine exercise by the Egyptian military and that what the pilot saw was probably a flare."