Grossman completed six of his first seven passes against the Dolphins before throwing a second-quarter interception.
Beck took over as the starter in October after a flurry of turnovers from Grossman in the Redskins' loss to the Philadelphia Eagles. The offense hasn't improved under Beck, however. The Redskins have scored only one touchdown in the past two games -- and that score came in garbage time against a San Francisco 49ers prevent-type defense.
Grossman began receiving more first-team work in practice, according to the source. Shanahan informed the team of the quarterback change over the weekend.
The Redskins, with personnel and injury issues on offense, lost all three of Beck's starts. He threw four interceptions to two touchdown passes in his four games this season.
Safety Oshiomogho Atogwe is active despite toe and knee injuries, but he's being replaced in the starting lineup by Reed Doughty. Redskins linebacker Perry Riley will make his first career start, replacing Rocky McIntosh.
Follow Jason La Canfora on Twitter @JasonLaCanfora.
The Associated Press contributed to this report.