Vizquel was seeking to tie Luis Aparicio's major league record for most games played at the position before Saturday night's game at Florida was rained out.
The game was rescheduled to be made up as part of a double-header on Sunday.
"Some things happen that you can't control," Vizquel said of the rainout.
Vizquel said he planned to play in Sunday's first game, and then would talk to Giants manager Bruce Bochy before deciding whether or not to play in the second game. Vizquel even suggested he could start the second game and come out after an inning.
Vizquel was activated from the disabled list on May 10. He missed all of spring training and the start of the season following off-season arthroscopic surgery on his left knee.
"I'm more concerned about my knee than the record," Vizquel said. "At this moment, my knee and being able to play all season is most important."
Vizquel, 41, has played 2,582 career games at shortstop and can tie and break Aparicio's record against the Marlins on Sunday.
"It's a historic moment," Bochy said. "He's excited, and we are, too. I'm proud of Omar, and I'm proud to say I'm here for it."
Vizquel, an 11-time Gold Glove winner, owns the major league record for most double plays (1,660) as a shortstop and the highest lifetime fielding percentage (.984) for players with at least 1,000 games at short.
He became the oldest shortstop (39) to win a Gold Glove in 2006 and his nine-year run of winning the award while playing in the American League from 1993-2001 is the longest streak by an AL shortstop since the award's inception in 1957.
Vizquel also begins Sunday as the active career hits leader with 2,609 and has the seventh most hits all-time by a switch hitter.
The teams waited 2 hours, 53 minutes before calling the game on Saturday night. Right-hander Matt Cain (2-3) will oppose Florida's Mark Hendrickson (6-2) in Sunday's first game. San Francisco left-hander Pat Misch (0-0) will start Game 2. The Marlins did not announce who would start the second game.
It was the first rainout at Dolphin Stadium three games in September 2004 were postponed because of Hurricane Frances.