The clip shows the U.S. president saying, in reference to Central American migrants, "they want to throw rocks at our military, [then] our military fights back".
The army's official Twitter account posted a video, "Please Watch and Make Your Deductions", showing Mr. Trump's speech on Thursday in which he said rocks would be considered firearms if thrown toward the American military at the nation's borders.
"We're not going to put up with that", Trump said in the clip.
"They want to throw rocks at our military, our military fights back", Trump said in his November 1 remarks.
"What I don't want is - I don't want these people throwing rocks", the president said, adding that if migrants throw rocks at troops there are "going to be problems". When they throw rocks like they did at the Mexico military and police, I say consider it a rifle.
The tweet was posted just days after clashes between Nigerian soldiers and Shia Muslims once again turned deadly.
Some of the criticism came from the US Embassy in Nigeria and Amnesty International.
The Nigerian director of defense, Brigade General John Agim, told the BBC the tweet was in reaction to Amnesty International's damning investigation, released on October 31, that found "excessive force" by soldiers and police led to the killing of at least 45 supporters of the Islamic Movement in Nigeria (IMN) over two days.
The Islamic Movement in Nigeria (IMN), otherwise known as Shiites, yesterday, vowed to continue their protest in Abuja, Nigeria's capital until their leader, Sheikh Ibrahim Elzazaky, is released unconditionally as directed by the court two years ago. IMN represents many members of Nigeria's Shiite minority and opposes the use of violence.
The Nigerian army reportedly used the words of President Trump to defend fatal shootings of Muslim protesters last weekend and Monday.
IMN members had clashed with soldiers in some parts of Abuja.
But only hours later, the Nigerian army tweeted out Trump's remarks the same day.
In the like manner, Executive Director of Amnesty International USA, Margaret Huang reprimanded the US President, Donal Trump for "encouraging and justifying human rights abuses" in his latest statements.
Agim said: 'The video was posted in reaction to the Amnesty International report accusing the army of using weapons against pacifist Shia protesters. What did David use to kill Goliath? Despite not being a traditional ally of the United States, the Nigerian military is taking notice and following suit.
The Army has previously tweeted photos of wounded soldiers who suffered from rock pelting religious protesters seeking the release of their detained leader.
Soldiers had arrived to assist police, a news release said, and were met with protesters who threw canisters of fuel, "large stones, catapults with risky objects and other unsafe items".