His decision comes a day after the new US president unveiled his plan to build a wall along the Mexico-US border.
Mr Trump also insisted the US would recoup the costs for the barrier from Mexico, which has strongly objected.
Senate Republicans said the US Congress would move ahead with the plan, and it would cost $12bn (£9.5bn) to $15bn.
Mr Pena Nieto announced that he had called off the 31 January trip after Mr Trump suggested he should do just that.
“If Mexico is unwilling to pay for the badly needed wall, then it would be better to cancel the upcoming meeting,” the US president wrote on Twitter on Thursday morning.
Earlier Mr Pena Nieto said he “lamented” the plans for the barrier.
“I regret and condemn the decision of the United States to continue construction of a wall that, for years, has divided us instead of uniting us.”
Mr Pena Nieto met Mr Trump – then a presidential candidate – in Mexico City in September and came under intense criticism at home. His approval ratings remain low.
Building a barrier along the 2,000 mile (3,200km) US boundary with Mexico was one of Mr Trump’s key pledges in the election campaign.
As he signed the directive at the Department of Homeland Security on Wednesday, He spoke of a “crisis” on the southern US border.
His executive orders also called for hiring 10,000 immigration officials to help boost border patrol efforts.
“A nation without borders is not a nation,” Mr Trump said. “Beginning today the United States gets back control of its borders.”
The executive orders are among a flurry expected on national and border security this week.
Mr Trump is next expected to announce immigration restrictions from seven countries with Muslim-majority populations in the Middle East and Africa. This could affect refugee programmes.
These countries are believed to be Syria, Iraq, Iran, Libya, Sudan, Somalia and Yemen.
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