Two-time tournament champion Djokovic has now won nine in a row over US players since losing at Wimbledon 2016 to Sam Querrey.
The world number one will be playing his ninth quarter-final here from 13 appearances at his home event; the win came a round after he claimed his 850th career victory against Philipp Kohlschreiber this week.
Fritz came to the court after defeating Jo-Wilfried Tsonga and Diego Schwartzman.
Djokovic turned in a steady performance with a dozen each of winners and unforced errors, while his opponent committed nearly 30 unforced errors in 68 minutes.
Defending champion Rafael Nadal was to play his second match of the pre-Roland Garros campaign when he faced Grigot Dimitrov in a third-round encounter.
Sixth seed Stefanos Tsitsipas earlier lost 6-2, 1-6, 6-4 as Daniil Medvedev continued his run of form.
The Russian winner will next line up against Djokovic after losing to the seed in January in the Australian Open fourth round.
Tsitsipas was caught on the back foot facing three match points as he trailed 0-40 on his serve late in the second set.
After saving the first two, the Greek mismanaged the third to seal his exit after an hour and three-quarters.
Medvedev increased his leading total of ATP season match wins to 20 as a result of his success as he beat Tsitsipas for the fourth time without a defeat in the series.
"This was a great achievement for me," Medvedev said. "Everything was perfect today.
"Some wind came up in the second set and I could not get used to it. But in the third, I just worked to put every ball in the court.
"I was pleased to fight back after going a set down in the third set."
The player who stands a career-high 14th credits his rising form to a renewed dedication to the sport.
"I've been working hard for the past 18 months - since before the start of 2018. I've dedicated my life to tennis, which I did not do before," he said.
"I had my best season last year - hopefully this year will be better."
The Russia reached his first quarter-final at the Masters 1000 level after winning his second match against a Top 10 opponent.
Tsitsipas, runner-up last season to Nadal in Toronto, suffered his eighth defeat of the season against 18 wins and will try and lift his game next week on the clay of Barcelona.
Results from the fifth day of the ATP Monte Carlo Masters on Thursday (x denotes seeding):
Daniil Medvedev (RUS x10) bt Stefanos Tsitsipas (GRE x6) 6-2, 1-6, 6-4
Guido Pella (ARG) bt Marco Cecchinato (ITA x11) 6-4, 4-6, 6-4