Friday marked one year since Russia invaded Ukraine and Odegaard wanted the club to show solidity with Zinchenko.
As a result, the Norwegian spoke to people at Arsenal on Friday about making Zinchenko captain for the match at Leicester on Saturday.
The Gunners went on to win the game 1-0, maintaining their two-point lead at the top of the Premier League over Manchester City.
“I spoke to some people in the club yesterday and then I went to Mikel and suggested it for him,” said Odegaard, when asked about giving the armband to Zinchenko.
“It was a nice thing to do to show him the support. It’s been a year now, too long, it’s a very difficult situation for him I know and very emotional.
“It was a good thing to do to show our support. I spoke to him this morning, asked if he was comfortable doing it.
“When he’s on the pitch he’s always 100 percent focused and always there. He doesn’t let him affect him but of course it’s not an easy thing for him, his family and everyone there. We just wanted to show him the support.
“We did a lot of the normal things, he always speaks before the games, I speak, others speak. It was the same today, before the game he said some words.”