The 30-year-old Serb released a statement on Instagram in which he said he respected the right of people to wear poppies.
The bombing, in 1999, was part of a Nato-led offensive to drive out Serbian forces from Kosovo.
Matic was the only United player not wearing a poppy during their 2-1 victory over Bournemouth on Saturday.
The Serb, 30, released a statement on Instagram in which he said he respected the right of people to wear poppies.
In his statement, Matic said: “I recognise fully why people wear poppies, I totally respect everyone’s right to do so and I have total sympathy for anyone who has lost loved ones due to conflict.
“However, for me it is only a reminder of an attack that I felt personally as a young, frightened 12-year old boy living in Vrelo, as my country was devastated by the bombing of Serbia in 1999.
“Whilst I have done so previously, on reflection I now don’t feel it is right for me to wear the poppy on my shirt.
“I do not want to undermine the poppy as a symbol of pride within Britain or offend anyone, however, we are all a product of our own upbringing and this is a personal choice for the reasons outlined.
“I hope everyone understands my reasons now that I have explained them and I can concentrate on helping the team in the games that lie ahead.”
Elsewhere, the Football Association and Stoke City are investigating a social media post by Potters winger James McClean in which he described some of the Championship club’s fans as “uneducated cavemen”.
The 29-year-old was abused by a section of the home crowd for not wearing a poppy during Saturday’s 0-0 draw with visitors Middlesbrough.