Trump had been scheduled to receive Enrique Pena Nieto at the White House on Tuesday.
Instead, the Republican president is managing a foreign policy spat with a normally friendly nation and key trade partner during his first week in office, AFP reported.
The escalating war of words over who would pay for the proposed border wall -- a central pledge made by Trump during his successful presidential campaign -- hit the breaking point on Thursday.
"If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting," Trump said on Twitter in the morning.
Under pressure at home to cancel the trip, Pena Nieto, who had good relations with former US president Barack Obama, tweeted later that he had informed the White House that he will "not attend the working meeting" next week.
Trump signed an order Wednesday for work to begin on building a wall along the 2,000-mile (3,200-kilometer) border.
But the US leader has struggled to articulate how the wall will be paid for, though he has suggested recently that the US would fund it first and Mexico would reimburse the cost later.