Passenger David Tellez said one of his young children spotted military aircraft touching down alongside their Aeromexico jet early on Thursday, Reuters reported, when the sound of gunfire suddenly rang out.
“As we were accelerating for take-off, we heard gunshots very close to the plane and that's when we all threw ourselves to the floor,” said Mr Tellez after the incident in the northern city of Culiacan.
A reporter with US news outlet ABC said at least one bullet hit the fuselage after the arrest of Mr Guzman and a senior member of the Sinaloa cartel.
Violence broke out on Thursday throughout Culiacan after the arrests.
Aeromexico said nobody on Mr Tellez's flight had been hurt.
The Culiacan airport closed shortly after the incident.
Burned vehicles could be seen across the city as security forces patrolled the city attempting to contain the violent backlash, Reuters said.
Mr Tellez, 42, was travelling with his wife and children aged seven, four and one after spending Christmas with family.
He told Reuters he had reached the airport for an 8.24am flight without incident, despite encountering road blockades set up after overnight shoot-outs.
Although Mr Guzman's arrest had not yet been confirmed, nervous security guards urged travellers to enter quickly.
“Authorities were not saying anything,” he said by phone.
Mr Tellez hid in an airport bathroom with his family after hearing that gang members were in the airport. The rumour turned out to be false and the Aeromexico travellers boarded quickly.
Yet, just as flight AM165 to Mexico City was about to take off, a succession of military planes landed on the airstrip.
Mr Tellez took out his mobile phone, recording several videos that show two large air force transport aircraft, smaller, fighter-like attack aircraft and military lorries on the tarmac. Then gunshots began to echo in the distance.
A video circulating on social media, appearing to capture the same incident, showed passengers crouching low below their seats as a child cried.
A flight attendant said the engine had been hit, triggering a leak. The crew directed passengers to disembark, moving them to a windowless waiting room in the airport.
It is not clear who was shooting at whom.
Mr Tellez's family plans to board another flight on Friday, but until then, is staying put.
“We prefer to stay at the airport until it's safe to leave,” he said. “The city is worse. There is a lot of shooting and confusion.”
'Atmosphere of uncertainty'
The Culiacan municipal government has warned residents not to leave their homes.
“The safety of Culiacan’s citizens is the most important,” it said.
Schools, local government and many private businesses closed.
Rev Esteban Robles, spokesman for the Roman Catholic diocese in Culiacan, said “there is an atmosphere of uncertainty, tension” and those who could were staying inside their homes.
“A lot of the streets are still blocked by the cars that were burnt,” Robles said.
Oscar Loza, a human-rights activist in Culiacan, described the situation as tense, with some looting at stores.
On the south side of the city, where Mr Loza lives, people reported convoys of gunmen moving towards a military base, but he said streets around his house were eerily quiet.
“You don’t hear any traffic,” he said.