Flight No 9W 536 landed under emergency conditions in the Omani capital safely at 2.50 pm IST and was taken to the isolation bay for passengers and crew to disembark.
Omani security agencies scanned the aircraft, passengers and baggage and, after a thorough search, the plane was cleared for take-off, a Jet Airways official said.
The tweet--"Bomb spotted on Jet Airways 9W 536 from Mumbai to Dubai departure at 1225 from CSIA (Chhatrapati Shivaji International Airport)-- triggered the scare after it was noticed by a Jet Airways staff, who informed Mumbai ATC about it.
The message was relayed to Muscat ATC at 1.55 pm following which the plane was diverted to the airport in the Omani capital.
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The tweet was said to have originated from the twitter handle of one Surendra Pratap.
Indian security agencies, including Mumbai police's cyber cell, have launched a probe.
"Jet Airways flight 9W 536, which departed from Mumbai at 1246 hrs for Dubai, was diverted to Muscat due to a bomb threat. The aircraft with 54 guests and 7 crew on board landed safely in Muscat at 1320 hrs local time (1450 hrs India)," Jet Airways said in a statement earlier in the day.