ITV4 commentator Jim Courier said the world No 1 was the champion driver of tennis in the best car after he outclassed Ricardas Berankis 6-1, 6-4, 6-1.
The Serbian superstar has yet to drop a set in reaching the Roland Garros last 16 for a record 12th consecutive year.
Djokovic’s streak of appearances at this stage surpasses the 11-year stint managed by both Rafael Nadal and Roger Federer between 2005 and 2015.
And Djokovic, who lives in Monaco and is a vegan like British F1 star Hamilton, said: “I’m honoured to be compared to Lewis. I respect Lewis and everything he does in his career.
“But also, off the court with his activism, trying to spread the awareness of animal slaughtering and animal protection and animal rights.
“Just diversity of his brand is fantastic, something that truly inspires me and a lot of athletes.
“I don’t want to talk about my driving next to Lewis’ name. I mean, honestly it’s embarrassing to speak about my driving, and in the same sentence with Hamilton.
“But I like to drive fast but I have to respect the rules, I was never racing.
“But the analogy and the comparison of my game with an F1 car, it’s definitely something that pleases me.”
Djokovic will next face Lorenzo Musetti after the Italian teenager beat his compatriot Marco Cecchinato 3-6, 6-4, 6-3, 3-6, 6-3.
He added to Eurosport: “I’m always my biggest critic and you can always do certain things better.
“It couldn’t be much better than this, especially the first and third sets. I served well, moved well and made him play.”
Musetti said: “We practised a lot with Djokovic together, so we know each other a little bit.
“For sure, there is going to be a little bit of tension, but I think it’s what I’m working for since my childhood.
“All the sacrifice and hard work I did in childhood became a reality now. So I’m just enjoying the moment, and I will try to do my best.”
Hamilton meanwhile starts second in Sunday’s Azerbaijan Grand Prix but is behind Max Verstappen in the F1 Drivers’ Championship standings by four points.