Foster was subsequently placed on the commissioner's exempt list, meaning he cannot practice or attend games but can be at the team facility on "a reasonable basis" for workouts, meetings and other permitted non-football activities.
The NFL will continue to review the matter.
Washington's decision to claim Foster was not unanimous, a source said. And there is no guarantee Foster will ever play for the team.
"The Redskins fully understand the severity of the recent allegations made against Reuben. If true, you can be sure these allegations are nothing our organization would ever condone. Let me be clear, Reuben will have to go through numerous steps including the full legal process, an investigation and potential discipline from the NFL, as well as meetings with counselors associated with the team before he will ever have the opportunity to wear the Burgundy and Gold as a player," senior vice president of player personnel Doug Williams said in a statement.
Washington was the only team to put in a waiver claim for Foster, a source told ESPN's Adam Schefter.
The 49ers selected Foster in the first round of the 2017 draft. The Redskins liked Foster before the draft but were concerned about his medical history.
Washington also has four defensive players who played with Foster at Alabama, including linemen Daron Payne and Jonathan Allen and linebackers Ryan Anderson and Shaun Dion Hamilton. Their insight into Foster helped the organization make the decision to claim him.
"We decided to investigate the situation with Reuben further by claiming his rights after candid conversations with a number of his ex-Alabama teammates and current Redskins players who were overwhelmingly supportive of us taking this chance," Williams said in the statement. "Nothing is promised to Reuben, but we are hopeful being around so many of his former teammates and friends will eventually provide him with the best possible environment to succeed both personally and professionally."
Foster was arrested in Tampa, Florida, on Saturday night, less than 24 hours before the 49ers faced the Buccaneers. Tampa Police said Foster and a woman were involved in a verbal altercation and that "Foster slapped her phone out of her hand, pushed her in the chest area, and slapped her with an open hand on the left side of her face." Police said a 1-inch scratch was observed on the woman's left collarbone.
According to the arrest report, the woman pressing charges against Foster for Saturday night's incident is Elissa Ennis, with whom Foster has been involved off and on for three years. It wasn't their first domestic incident. On Feb. 11, he was arrested on suspicion of domestic violence and possession of an assault rifle; a loaded Sig Sauer 516 rifle was discovered on a bathroom floor. The domestic violence charge was dropped in May when Ennis recanted her allegations that Foster had hit her. But Foster pleaded no contest to a misdemeanor weapons charge and was given two years of probation and banned from possessing guns during this time.
In addition, Foster served a two-game suspension to start this season, stemming from an arrest for misdemeanor marijuana possession in January (charges were dropped after he completed a first-time-offender diversion course). He also failed a drug test at the 2017 NFL combine and was sent home early after getting into a heated argument with a hospital worker. Foster was considered a top-10 talent, but his off-field issues and medical concerns caused him to drop to the 31st pick.
Foster missed six games with injuries his rookie season but finished second on the team with 72 tackles. He appeared in only six games this season and recorded 29 tackles. The Redskins have started Zach Brown and Mason Foster at inside linebacker all season but clearly want to upgrade the position moving forward.
Washington also signed running back Adrian Peterson in August. Peterson was suspended for all but one game in 2014 after being charged with felony child abuse; he eventually pleaded no contest to a reduced charge of misdemeanor reckless assault.
Foster, 24, was arrested at 9:10 p.m. local time Saturday and booked into Hillsborough County Jail at 11:11 p.m., according to a custody report from the Hillsborough County Sheriff's Office. He was released Sunday afternoon on $2,000 bail.