As a result, it will no longer feature in the app’s Discover section. The firm said it would “not amplify voices who incite racial violence and injustice”.
The decision follows Mr Trump saying that “vicious dogs” and “ominous weapons” would have been used on protesters if they had breached the White House fence.
It follows Twitter’s decision to hide some of the president’s posts.
Snapchat said: “Racial violence and injustice have no place in our society and we stand together with all who seek peace, love, equality, and justice in America.”
The move is likely to feed into tensions between the White House and social media, which escalated when Twitter added fact-checking tags to some of the President’s tweets last week.
The president subsequently signed an executive order seeking to curb legal protections offered to the industry.
Twitter later hid one of the president’s tweets for breaking its rules on “glorifying violence”.
Snapchat’s action will also put further pressure on Facebook.
Its chief executive Mark Zuckerberg has resisted internal and external calls to intervene in regard to posts on its platform. Mr Zuckerberg has said the firm’s free speech principles mean the president’s posts should be left up unaltered.
President Trump has more than one million followers on Snapchat, according to the Bloomberg news agency, and his account will not be suspended or deleted.
However, the fact it will not feature in Discover means that his posts will only be seen by people who subscribe to or search for his account directly.
The offending comments that Snapchat cited to US media as cause for its move were not posted on the Snapchat platform.