Sharapova, who won the Tianjin Open two days ago, brought her usual power but lacked accuracy with some wild swings on key points.
"I felt fine physically, to be honest, especially after having played five matches in five days (in Tianjin). That was a big surprise," Sharapova said. "Maybe I wasn't as prepared as I should have been. ... Maybe if this tournament hadn't been in Moscow, I wouldn't have played it."
Sharapova was under pressure on serve from the start and saved six break points before finally being broken for 6-5. She responded by breaking Rybarikova, but Sharapova's double fault at 4-3 in the tiebreaker handed the Slovakian the momentum to close out the set.
Rybarikova, seeded eighth, sealed the match after saving two break points to lead 5-4, then breaking Sharapova in the next game. Rybarikova will play Alize Cornet in the second round.
Six months after she returned from a 15-month doping ban, Sharapova is still trying to move back up the rankings from her current position of 57th. Her first tour appearance in Moscow in a decade drew a large and enthusiastic crowd despite taking place in the afternoon.
Also, another Russian title hopeful fell in the first round as fifth-seeded Anastasia Pavlyuchenkova lost to unseeded compatriot Daria Kasatkina 7-6 (2), 6-1.
Last year's finalist, Daria Gavrilova of Australia, reached the second round, beating Kristyna Pliskova 6-4, 6-7 (5), 6-1.
Seventh-seeded Julia Goerges beat Russian qualifier Polina Monova 6-0, 6-3.
In the men's Kremlin Cup, sixth-seeded Damir Dzumhur defeated Thomas Fabbiano 6-3, 0-6, 6-2. Andrey Rublev, seeded fifth, was a first-round loser to qualifier Filip Krajinovic 7-5, 7-6 (6).