The clash comes after a US prosecutor alleged last week that Hernandez took millions in bribes from drug lords, including jailed Mexican kingpin Joaquin "El Chapo" Guzman, during a trial for Hernandez's brother.
About a thousand protesters gathered in Tegucigalpa's central park shouting slogans against the president, when dozens of police officers arrived and tried to force them to disperse.
Some of the protesters fought back, attacking police with stones from under a cloud of teargas.
The anti-Hernandez demonstration was called by a coalition of civil society groups and took place just hours after a march in which more than 6,000 Hernandez supporters were estimated to have participated, according to journalists.
Many of the supporters chanted "Viva JOH (Juan Orlando Hernandez)!" and "He's not alone."
Honduras has been rocked by the allegations against Hernandez -- who has long presented himself as a champion in the campaign against drug trafficking.
"The Honduran people are good and have been with me in good times and in bad times" Hernandez said in a speech to his supporters.
A country of 9.4 million plagued by gangs, poverty and corruption, Honduras has witnessed recent violent protests over the president's controversial health and education decrees.
When US prosecutors alleged in court documents made public in August that the president was part of the conspiracy in which his brother was charged, it brought crowds onto the streets demanding he resign.