Several buildings were set on fire after protests and riot police clashed with demonstrators while attempting to disperse the crowd with tear gas and water cannons.
"The narco must go, JOH must go!" protesters chanted, using the president's initials, as they marched through central Tegucigalpa toward Congress.
A court filing was published late last week in which U.S. prosecutors alleged that Hernandez's 2013 presidential bid had been partly funded by money from drug traffickers.
The document filed to the U.S. Southern District Court of New York said the Hernandez campaign received US$1.5 million from "drug proceeds" that were used to bribe local officials in exchange for protection and the completion of public works.
A conservative ally of the United States, Hernandez has come under increasing pressure since his younger brother Tony was arrested in Miami in November on drug trafficking charges.
At that time, Hernande said no one was above law. However, his link to drug trafficking was revealed last week when a court document on his brother’s case was declassified.
The document said a “co-conspirator 4,” later referred to as CC-4 conspired to use US$1.5 million to bolster CC-4’s presidential campaign.
JOH was said to be CC-4 in the document. Even though he rejected the allegations, protesters called him “narco dictator” Tuesday demanding his resignation.
Hernandez cast himself as the victim of a smear campaign by drug gangs he had targeted, and accusing political opponents, such as ex-president Manuel Zelaya, of colluding with gangsters to discredit him.
Protesters attacked police with sticks and stones near Congress after officers deployed tear gas, and a Red Cross official said that five people were treated for injuries.
Fire service spokesman Cesar Trochez said "three commercial businesses caught fire" during the clashes, adding that the causes for the blazes were under investigation.
The demonstration against Hernandez was called by the Platform for the Defense of Education and Public Health, a coalition of trade unionists and public workers that have sought the president's ouster over his plans for public services.