Russell finished 240 thousandths ahead of Hamilton and Spaniard Carlos Sainz (Ferrari) was third. Next came the McLarens of Lando Norris and Daniel Ricciardo.
The Monegasque Charles Leclerc (Ferrari), third in the championship, had to settle for sixth position, ahead of the Mexican Sergio Pérez (Red Bull), second overall, who was seventh.
During the session, solid World Championship leader Verstappen (Red Bull) spent most of the time in the garage due to a gearbox problem ten minutes into the session.
The incident caused the only red flag of training, while the car of the Dutchman, who competes at home this weekend, was moving.
The second practice session is also scheduled for this Friday. The organization has not specified whether Verstappen will be able to participate.
‘Mad Max’ will seek his fourth consecutive victory on Sunday in front of his public, which could give him an almost definitive push in preserving the world title he achieved last year.
This is how the Top 10 of the first free practice session ended:
George Russell (GBR/Mercedes) 1:12.455 (29 laps)
Lewis Hamilton (GBR/Mercedes) 1:12.695 (28)
Carlos Sainz Jr (ESP/Ferrari) 1:12.845 (30)
Lando Norris (GBR/McLaren-Mercedes) 1:12.929 (32)
Daniel Ricciardo (AUS/McLaren-Mercedes) 1:13.077 (31)
Charles Leclerc (MON/Ferrari) 1:13.127 (30)
Sergio Perez (MEX/Red Bull) 1:13.416 (30)
Fernando Alonso (ESP/Alpine-Renault) 1:13.633 (31)
Esteban Ocon (FRA/Alpine-Renault) 1:13.963 (33)
Alexander Albon (THA/Williams-Mercedes) 1:14.063 (29)