The 23-year-old Nigerian international fainted and slumped to the Stade Velodrome pitch in the early stages of the 2-2 draw played in 30-degree heat on Sunday.
"All the additional examinations performed on Tuesday did not reveal any cardiac abnormalities," Bordeaux said in a statement, before adding he could be ready to play against Angers on Sunday.
Worried teammates gathered around the stricken Kalu and frantically waved their hands to the bench to summon medical help. He briefly played on but was replaced by Remi Oudin.
The incident came just two months after Denmark's Christian Eriksen suffered a cardiac arrest in a Euro 2020 match.
"With what happened with Eriksen at the Euros, we think about it. Everyone got a little scared. Fortunately, it ended well," said Oudin, who went on to score, after the match.
In June 2019, Kalu was also hospitalised after suffering from dehydration while training with Nigeria in the Egyptian heat during the Africa Cup of Nations.