"Regarding the game that will take place in the Paris region, the head of police has considerably strengthened security," French Interior Minister Gerald Darmanin told reporters at a press event on Olympic Games security.
Paris-St-Germain are due to play Barcelona in Paris on Wednesday night.
"We have seen, among other things, a communication from the Islamic State that particularly targets stadiums. It is not new," he added.
Islamic State was alleged to have threatened four venues for this week's Champions League matches, including the Parc des Princes in Paris and two games in Madrid hosted by Real Madrid and Atletico Madrid, who face Manchester City and Borussia Dortmund respectively.
In London, Arsenal take on Bayern Munich in their quarter-final on Tuesday night.
"We're aware of online and media reports in relation to calls to target matches across Europe and here in London," London's Metropolitan Police said.
"However, I want to reassure the public that we have a robust policing plan in place for tonight's match."
Spanish police forces will deploy 2,000 extra officers to boost security in the capital for the two games, government spokesperson Pilar Alegria told reporters on Tuesday.
She said the terrorism alert level had been raised to four on a scale of five.
Spain has kept its state of terror alert at level four - the second-highest on a five-point scale - since Islamist militant attacks in Paris in June 2015.
Islamic State has claimed responsibility for the recent attack on a Moscow concert hall that killed at least 143 people.
