"I wouldn't travel on a helicopter with John Key," Luxon said.
Key was unfazed about this apparent dig.
"The good news is if he changes his mind and does come for a fly I won't have to worry about him pulling his hair out," Key said.
Key was not the first one to raise Luxon's baldness on Tuesday - with Luxon himself taking a crack.
When asked to describe himself, Luxon said he was a "good-looking bald man".
"He's a big-picture thinker who is enjoying doing what he's doing," Luxon said.
When asked to describe himself in one word, Luxon said he was a "big-picture thinker", before realising that was more than one word.
"That is three words - I'd like to make it 'strategic'".
Luxon said he was learning the ropes of being an MP, downplaying suggestions he might have his eye on the leadership.
"I've only been in Parliament 12 months. I keep saying to you guys [the media] all the time that I'm here to learn. There are four things to master if you're going to build a long-term career in politics.
"The first is that you've got to understand your electorate; you've got to understand your party; the Parliament here is an odd beast to get your head around over time and then really start to get into policy areas, and that's what I've been doing around Three Waters."
Luxon reiterated this week that none of his colleagues had approached him about having a tilt at the leadership.
