Crowell will undergo season-ending surgery next week, the source said.
Crowell had signed a one-year deal worth up to $2.5 million, according to sources.
The injury is the latest blow to the Raiders' depth chart at running back. Last week, Marshawn Lynch indicated that he's done playing football. Doug Martin was the team's leading rusher last season, but he was a free agent.
The Raiders used the No. 24 pick in the draft on Alabama running back Josh Jacobs and also have Jalen Richard, DeAndre Washington,James Butler and Chris Warren on the roster.
Crowell became a free agent when he was released by the New York Jets on March 14, a day after the team agreed with running back Le'Veon Bell on a four-year contract.
Crowell, 26, was one-and-done with the New York Jets. After four seasons with the Cleveland Browns, he signed a three-year, $12 million contract ($4 million guaranteed at signing) and became the starting running back last season.
He rushed for 685 yards, six touchdowns and a 4.8-yard average, but it was an odd season in that one-third of his production came in one game. In a Week 5 victory over the Denver Broncos, he set the franchise record with 219 rushing yards.
The most amazing part about it was he needed only 15 carries -- a remarkable 14.6 per-carry average. It was the highest average in a game (minimum: 15 attempts) by any player in NFL history.
Crowell's season dipped sharply after his record-setting day, as he eclipsed 49 yards only once for the remainder of the year. He battled foot and ankle injuries and finished on injured reserve.
He created national headlines with an unsportsmanlike-conduct penalty in Week 3 at Cleveland. After scoring against his former team, Crowell celebrated by pretending to wipe his rear end with the ball, which he threw into the ground.
Crowell received a public rebuke from then-coach Todd Bowles. He was fined $13,369 by the NFL, but he parlayed the crude gesture into an endorsement deal with a company that sells toilet wipes for men.
In 2016, Crowell sparked a controversy when he posted on his Instagram account an illustration of a police officer being stabbed in the neck by a hooded figure. It was his response to the fatal shootings of two black men by Dallas police officers. A day later, five officers were killed by sniper fire. Crowell later apologized and donated a game check to the police department.
In five seasons, Crowell has 3,803 rushing yards and 27 touchdowns.
ESPN's Paul Gutierrez, Jeff Legwold and Rich Cimini contributed to this report.
Crowell injury changes Raiders' timetable with Jacobs
Jeff Darlington examines the effect RB Isaiah Crowell's Achilles injury will have on the Raiders' depth chart.