Mazraoui reportedly cited his Muslim faith as the reason behind not wanting to join the initiative, which resulted in his teammates also not wearing the jacket - so that the defender was not seen as the sole individual not supporting the cause.
This comes after Ipswich captain Sam Morsy refused to wear a rainbow armband, with the Egyptian also attributing his Muslim faith as the reason for not taking part in the Premier League's 'Rainbow Laces' campaign.
In a statement to The Athletic, Manchester United said that they welcome fans from all backgrounds but also that players are entitled to hold their own opinions.
"Manchester United welcomes fans from all backgrounds, including members of the LGBTQ+ community, and we are strongly committed to the principles of diversity and inclusion.
"We demonstrate these principles through a range of activities, including support for our Rainbow Devils supporters' club, and campaigns to celebrate our LGBTQ+ fans and combat all forms of discrimination.
"Players are entitled to hold their own individual opinions, particularly in relation to their faith, and these may something differ from the club's position."
United have been involved in the Rainbow Laces campaign both in previous seasons and the current campaign, with Bruno Fernandes wearing a rainbow armband while also speaking to the club's website about the need for supporters to feel included.
A video was also uploaded on their website of players Harry Maguire and Jonny Evans speaking with members of the Rainbow Devils fan group.
You can read more about the Premier League's Rainbow Laces campaign here.