The NHL's reigning MVP, who has missed only one game in his four-year career, caught a flight home Monday morning.
Ovechkin, who led the league in goals and points last season, will sit out Washington's game against the visiting Nashville Predators on Tuesday night. The Capitals don't play again until Saturday at the Buffalo Sabres.
The Capitals say they do not know when he will be back.
"I'm sure we'll know more as the week goes on," coach Bruce Boudreau said.
Ovechkin will be replaced on the top line by Brooks Laich.
Ovechkin, who led the Capitals to a Southeast Division title last season, has two goals and three assists through eight games this season.
The star left wing discussed the situation and his trip with general manager George McPhee on Sunday night.
"He had to go and he wanted to be near [his grandfather], but if you know Alex, he doesn't want to leave his teammates," Boudreau said. "So that's always a struggle, but in the end, he knows what he needs to do -- and that's family first."
Information from The Associated Press was used in this report.