Bayern Munich forward Kane struggled with a back injury towards the end of the season and only played the final 30 minutes of England's 3-0 win over Bosnia and Herzegovina on Monday, netting the third from close range.
"Toney will be involved in the game on Friday but I have got to get Harry Kane right,” said Southgate, who has to whittle down his squad to 26 players by Friday.
"So sometimes the priorities of what’s required and what you would like to see as well, you can’t achieve all of those objectives. Simple as that."
Southgate said Friday's game at Wembley takes on added significance as it is their final warm-up for Euro 2024 in Germany.
"We want to build on (Monday's) performance, physically it’s an important game for players," he added.
"Even for players who have played a lot of football they still need rhythm of playing matches.. Friday becomes an important exercise for us."
England open their campaign on June 16 against Serbia in Group C.