Protesters marching to the congress building, also exchanged a volley of rocks and bottles with small groups of pro-Chavez demonstrators.
Several people were slightly injured during the clashes, witnesses said.
"With this reform, the president is going to control everything. His power will be almost unlimited," said 22-year-old Adolfo Rengifo, one of the protesters.
Marchers wore T-Shirts with the word "No" to symbolise their negative vote on an upcoming referendum to approve the constitutional changes, though analysts say Chavez is likely win the election.
"The message to the congress and to the government is that there is ... a part of this country that rejects these reforms and we want to be heard," Stalin Gonzalez, a student leader, told a local television station.
A student delegation delivered a document to congress criticising Chavez's proposed constitutional rewrite.
'Unacceptable'
Chavez's plans have also drawn criticism from opposition politicians and Venezuela's Roman Catholic church, who say he is seeking to increase his power.
Even the pro-Chavez party, Podemos, has criticised the changes, especially the proposal to lift restrictions on the number of presidential terms Chavez can hold.
But Chavez says the changes will enable him to help the country's poor majority with reforms such as extending social security benefits.
"They say the reform is morally unacceptable. They are the ones who are morally unacceptable," Chavez said on Sunday, referring to criticism from Catholic leaders.
A referendum on the proposed changes is due in December.