The 19-year-old left-hander's dream run in Paris was ended emphatically by Australia's Ashleigh Barty on Saturday, Vondrousova going down 6-1 6-3.
Mandlikova was also 19 when she claimed the French Open, having already won the Australian Open title.
She believes Vondrousova can emulate her and become the new face of Czech tennis.
"I definitely think that," Mandlikova told Reuters. "After Petra Kvitova and Karolina Pliskova, Marketa is now the one to look for. She's already an awesome player and she definitely has it in her to win a Grand Slam.
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"She just needs to work on mental toughness and just keep working hard on adding different elements to her game."
Despite not being seeded, Vondrousova's run to the final was not a total shock considering her claycourts skills and the fact she has been the most consistent player on the WTA Tour since bowing out in the second round of the Australian Open.
Her world ranking will rise to 16 on Monday and Mandlikova says the hard part for her will be that she is now a name, and her tricky game and deft dropshots will no longer be a surprise.
"It's always easier when you're a brand new face and have just appeared," the 57-year-old said. "I'm not putting her game down because she has a talent, she has great hands.
"She has lots of tools and other players don't really know what they are or how she uses them, although Barty got her tactics spot on today.
"I think the same thing happened with (2017 French Open champion) Jelena Ostapenko. She came here and hit bullets from everywhere and the girls didn't know where they were going."
While a different sort of player to herself, Mandlikova, who was known for her serve and volley, believes Vondrousova can also be a threat at Wimbledon.
"With her great hands she can play on grass very well, I think. She will use her slice and her lefty serve."
Vondrousova said Barty had not let her play her game, but said the past fortnight would "change her life", adding: "Of course I'm a little bit sad now, because I lost. But it was a great two weeks.
"It's gonna be a bit strange because I'm going to be a seed at Grand Slams. A lot of things are going to change now, but I just can't wait to get back home and see what's gonna happen," she told reporters.
(Reporting by Martyn Herman; editing by Tony Lawrence)
