“Co-operation, yes; intervention, no,” Andrés Manuel López Obrador said in response to Mr Trump’s comments.
The US president announced in a Tuesday interview he would legally designate Mexican drug gangs as terrorist groups.
Earlier this month nine US citizens were killed in an ambush in Mexico.
The victims – three women and six children who also had Mexican nationality – were killed while travelling through a remote area in the north of the country.
After the attack, the victims’ Mormon community – the LeBarons – petitioned the White House to list the cartels as terror groups.
The legal move outlined by Mr Trump would enable a wider scope of action against them.
Speaking at a news conference in Mexico City on Wednesday, President López Obrador said Mexicans “had nothing to fear” and that the foreign minister, Marcelo Ebrard, would address the issue after the US Thanksgiving holiday on Thursday.
On Twitter, Mr Ebrard said he was already in contact with US authorities and that his efforts would be focused on “defending [Mexico’s] sovereignty and its own decisions”.
Earlier, he said Mexico “would never accept” any violation of its sovereignty and that the government was committed to tackling transnational organised crime, adding: “Mutual respect is the basis for co-operation”.