Kane played 22 times for Tottenham Hotspurs before the start of the World Cup, completing the full 90 minutes in all but three of those games.
The 29-year-old won the golden boot at the Russia 2018 World Cup but is yet to get on the scoresheet or register a shot on target after two matches in Qatar.
England started their campaign with a 6-2 drubbing of Iran but could only manage a goalless draw against the USA in their second game.
Shearer has opined it might be time for England manager Gareth Southgate to allow the national team captain catch a breather.
Shearer said in his BBC column: "I am not overly concerned about that statistic [Kane not having a shot on target], because we know the provider role Harry plays for this England team, even when he is not scoring himself. But watching him against the United States, it was clear something wasn't right.
"He came through that scare about his ankle before the US game but, after playing a big part in an impressive team performance in the Iran game with two assists, he looked very tired and very leggy to me.
"It might be time to think about getting him right for the knockout stages, and I have a sneaky feeling Callum Wilson might come in to face Wales on Tuesday instead.
"England need to freshen things up anyway, to get the feel-good factor back after the disappointment of our draw with the US, and restore a bit of confidence."
