NFL Network's Ian Rapoport reported Tuesday that the injury occurred when Stafford hit his thumb on another player's helmet. Stafford underwent X-rays that came back negative, and he is only expected to miss a few days.
The 33-year-old signal-caller is set to enter his first season with the Rams after spending his first 12 NFL campaigns with the Detroit Lions.
L.A. dealt quarterback Jared Goff, two first-round picks and a third-round pick to the Lions this offseason in exchange for Stafford.
The Lions selected the former University of Georgia star with the No. 1 overall pick in the 2009 draft. Stafford excelled in Detroit, throwing 282 touchdown passes to just 144 interceptions in 165 regular-season games.
Although Stafford never won a playoff game in Detroit, the Rams acquired him in hopes that he could get them back to the Super Bowl within head coach Sean McVay's innovative offense.
Now he's started the second act of his NFL career in Los Angeles, a Super Bowl-contending team on paper with Stafford in the mix.
John Wolford is the Rams' backup option and Bryce Perkins sits No. 3 on the depth chart, but it doesn't appear as though they'll be counted on to take starter's reps for long.