Kane was dealing with the back issues ahead of the second leg of Bayern's Champions League semi-final against Real Madrid last week but played through the pain.
The England captain's injury setbacks have surfaced weeks before the European Championship begins on June 14 in Germany.
"Harry is in medical treatment with his personal doctor. He can't travel with us" to Hoffenheim, Tuchel told reporters on Friday. "It was already questionable in Madrid, as you might have noticed.
"We tried it with injections and therapy, but his back was cramping. It got even worse and he could feel it in everyday movements. There was no chance for him to even train."
England are grouped with Slovenia, Denmark and Serbia at the Euros. Coach Gareth Southgate will name his preliminary squad for the tournament on Tuesday.
Kane, who also missed Bayern's previous league game against Wolfsburg with injury, has scored 44 goals for across all competitions in his first season at the German club, including four hat tricks in the Bundesliga.