Bardem, married to Penélope Cruz, made the gaffe at a press conference in Paris to promote the documentary Sons of the Clouds: The Last Colony.
Directed by fellow Spaniard Álvaro Longoria, it tells of human rights abuses in a former Spanish colony, the Western Sahara, which was annexed by Morocco in 1975.
Alluding to the idea that Paris had ignored the abuses, Bardem mentioned a conversation he claimed to have had with France's United Nations ambassador in the US in 2011.
He claimed that the ambassador had described Morocco as, "A mistress with whom we sleep every night, even if we are not particularly in love, but whom we must defend. In other words, we turn a blind eye."
The comments were reported by French newspaper Le Monde and created an immediate stir in Morocco.
Demonstrators crowded around the French embassy on Tuesday, waving flags and shouting "Ambassador coward!" and "Morocco cannot be humiliated!"
Mustapha Khalfi, Morocco's Minister of Communications, demanded explications "beyond a simple statement from the Ministry of Foreign affairs to repair the damage caused by these words, whether they have been falsely attributed or whether they have been spoken truly."
Khalfi went on to describe the comment as "scandalous and unacceptable".
The Oscar-winning actor's comments inflamed already high tensions between the two countries. They have recently clashed over torture allegations, leading French police to question Moroccan officials in their Paris embassy.
President Hollande had to intervene after Bardem's comments, according Spanish daily El País.
The French President telephoned King Mohammed VI in what French described as "a message of confidence and friendship to Morocco" and added that "the misunderstandings have been cleared up".