A number of users commented under Martial's Instagram posts with racist messages and symbols mere days after the company said it was going to impose stronger penalties on accounts found to be sending abuse.
A number of players and clubs have spoken out to condemn the racist abuse received by players after games.
"We condemn the racist abuse that too many players, officials and supporters continue to encounter, most recently on social media platforms," the statement said.
"We stand shoulder to shoulder in saying there is no room for racism, hate or any form of discrimination in our beautiful game. It should not happen and it must stop."
Facebook, who own Instagram, committed to tougher measures against accounts sending hate on Feb. 10 and said they were "horrified" at what players were receiving.
"I'm horrified at the type of abuse that people, especially these footballers, have to deal with on the basis of who they are, whether it's their race or their religion or their gender, and as a company, we're disappointed to see that sort of behaviour that plays out offline also playing out on our platform," Facebook head of content policy Fadzai Madzingira told the BBC.
"It's why we're making the announcements today about taking tougher measures to go after accounts that are violating our community standards and our goals within Instagram direct messages."
The Premier League has also announced a plan to eradicate racial prejudice and create more opportunities for minority ethnic groups in football.