"The injury is not a serious one but it is serious enough to keep him out of the match," Tena said at his pre-match briefing with reporters.
"He lives in London, he plays for a team in London and naturally had a dream of playing for the gold medal for Mexico in London, but the dream is over for him.
"It will take about two weeks to fix up and he will return to his club (Tottenham Hotspur) on Monday to start his rehabilitation," he added.
Tena would not be drawn on who would replace the 23-year-old who has scored three goals as Mexico made it through to their first Olympic final. Their previous best Olympic placing was fourth in the Mexico City Games in 1968.
Tena said that Saturday's final against the favourites was "the most important match of my career" but that he would not change the team's style to cope without Giovani.
Their opponents boast a very strong team which includes Neymar, Oscar and the tournament's top scorer Leandro Damiao, who has scored six of Brazil's 15 goals to date.
Brazil coach Mano Menezes, speaking at Wembley after a familiarization visit of the stadium, told reporters: "If you had a chance to write a plot for a film about winning a gold medal, you could not choose a better place for it than Wembley."
Brazil, like Mexico, are chasing their first Olympic soccer gold, something of an obsession back home after a series of failures going back to 1952.
Brazil have two soccer bronze medals and two silvers after losing in the 1984 and 1988 finals, and Menezes, who is also the coach of the senior side, is under considerable pressure to bring back the Olympic title for the first time.
"You do have butterflies in your stomach, that is part of it and the day I don't have them is the day I should not be working in football," he said.
"I do feel under pressure, but it is no different to any other moment in these Olympic Games. This is our third opportunity to win gold and we are going to take what we've learned from those two defeats and hopefully win on Saturday."