Johnson, the third-round pick out of Miami, suffered a hamstring injury on a running drill in 11-on-11s, and West came up limping with a calf injury about 15 minutes later.
Browns owner Jimmy Haslam said in a press conference after practice that the backs "might be out a little bit.''
In addition to Johnson and West, running back Glenn Winston is still idle with his knee injury.
That leaves Isaiah Crowell, Shaun Draughn and Luke Lundy to divide up most of the reps, the story said. It's not yet known how long Johnson and West will be out, but the Browns have Monday off, which will give them a chance to rest up. The injuries have given third-year back Shaun Draughn a chance to prove he deserves a roster spot. Draughn, signed by the Browns as free agent last December and re-signed in March, has been churning up yards and catching passes out of the backfield, the story went on to say. The situation could especially benefit Crowell, who had flashes of success last year. Johnson's chances of earning the starting job could be hurt the longer he misses reps. The Browns RB situation is shaping up to be another head-scratcher for fantasy owners this season.