The Thomson Airways flight from London Stansted airport to the Red Sea resort came within 300 meters (1,000ft) of a missile as it neared the Egyptian airport on August 23.
The pilot took timely evasive action after the missile was spotted in its trajectory, 'The Guardian' reported.
The crew of flight TOM 476 landed the plane safely and passengers were not advised of the incident.
The airline said the crew reported the missile near-miss to the UK's Department for Transport (DfT) immediately after conducting an assessment upon landing in Sharm el-Sheikh, in line with established protocol.
"The DfT conducted a full investigation in conjunction with other UK government experts. After reviewing the details of the case, the investigation concluded that there was no cause for concern and that it was safe to continue our flying programme to Sharm el-Sheikh," a DfT spokesperson said.
Airlines are currently prohibited from flying below 26,000 feet over the Sinai peninsula due to fears that Islamic State militants fighting the Egyptian government could have weapons capable of bringing down a plane.
However, it will underline fears that regional instability could threaten flights, as more countries joined Britain in restricting air travel and imposing tougher security measures.
According to the latest reports, black box data from the Russian plane that crashed in Egypt indicate it was bombed.
Sharm el-Sheikh is a popular destination with the UK and Russian holidaymakers.