Kane suffered a knock to his after a tackle by Iran's Morteza Pouraliganji early in the second half of England's 6-2 opening win in Group B and was replaced late on.
The Football Association confirmed that the striker, whose 51 goals for his country is just two behind Wayne Rooney's record, had undergone a scan, but Pickford offered an upbeat assessment.
"Yeah I think he's good, obviously a little but sore, but I think he's fine, he was out on the grass with us," goalkeeper Pickford told reporters at England's training base.
"It's good because he's our captain."
The possibility of Kane's well-chronicled ankle injuries returning during a World Cup that has started in almost perfect fashion for England will be a worry for coach Gareth Southgate.
Although on the flip side, five England players found the net against Iran with Bukayo Saka scoring twice and teenager Jude Bellingham notching his first international goal.
Kane remains England's talisman, however, having won the Golden Boot at the 2018 World Cup with six goals as England reached the semi-finals before losing to Croatia.
Southgate would be unlikely to risk a less than 100% fit Kane against the United States on Friday, when a win could send them into the last 16 with a game to spare, preferring to make sure he is ready for the latter stages of the tournament.
If so, Pickford is confident England have enough quality in the squad to make do without their skipper.
"I think everyone took their chance when Harry came off, Callum (Wilson) came on and played really well and got the assist for Jack (Grealish) and was very unselfish.
"Everyone's training really hard and everyone's here for a reason," the Everton stopper said. "But obviously Harry is an unbelievable player, he sets an example in the squad.
"He's the leader, he's the captain and we all look up to him but there are opportunities for the other lads too."
Defender Kyle Walker, who was not deemed fit enough to play against Iran after recovering from groin surgery, trained on Wednesday and could be an option for Southgate.
England's final Group C match is against Wales.
