She told Rt Revd Dr Angus Morrison "your jewellery is better than mine" as she met him at the Scottish Parliament.
Footage of the discussion will be shown on a BBC documentary about the church leader on Thursday.
It includes contributions from all of Scotland's political party leaders.
In one scene the moderator is shown with the first minister wearing his gold ring and cross pendant which is given to every Church of Scotland leader.
Ms Sturgeon said: "It's always a really valuable opportunity to discuss matters of concern to the Church, often the same issues that are of concern to the government and the current Moderator. The current Moderator has been fantastic in his role."
Scottish Conservative leader Ruth Davidson said: "This particular Moderator is both a joy and a rogue, having spent some time with him abroad.
"Each Moderator makes of the job something of themselves, they bring themselves to the table, so it is a different relationship with each one but it is no less special for that."