The scene shows a rugby player, All Black Richard Kahui, rejecting a chance to kiss gay Air New Zealand flight attendant Will Coxhead on the cheek, The Dominion Post reported.
David Morgan, the airline's operations and safety manager, said the video "Crazy About Rugby," filmed in a cockpit, had been well received.
"When we created this video and discussed the scene featuring a gay male flight attendant and a rugby player with key stakeholders, including a number of the gay community, we received none of the feedback we have in the past week," Morgan said.
The airline would not name the complainants.
Gay Member of Parliament Grant Robertson said he had viewed the video many times without being offended.
"I took it in the spirit of fun. But I can certainly understand some people might be concerned about it. Air New Zealand are behaving responsibly here," he said.
Coxhead, the flight attendant, said, "There are some people in the gay community that can be a little precious and need to lighten up."