Authorities say 15 protesters were arrested.
Police fired tear gas and used truncheons against some 1,000 demonstrators after they started to block the highway that links Baku to the coastal city of Alat.
Some demonstrators threw stones at police and continued to block the highway for almost two hours before the protest was dispersed.
The owners of the shopping center, which reportedly has indirect ties to state officials, claimed that the demonstrators were mainly protesting a new law that requires all retail shops to use cash registers.
But shopkeepers at the privately owned Bina shopping center who attended the January 19 rally told RFE/RL they were angry about rent increases of up to $300 a month and other fees that they say could put them out of business.
"They are raising the rent by around 250 manats," or about $310*, one protester said. "We are demanding our rights. And they also collected 5,000 manats more. Everybody knows that. Now they want additional 3,500 manats."
The Interior Ministry has denied media reports claiming that police fired rubber bullets at the protesters.
The ministry told RFE/RL that the Baku Prosecutor's Office has launched a criminal case over the clashes. It said 10 police officers were injured and some demonstrators also were wounded in the violence. Local media reports said some protesters were beaten.
About 5,000 shopkeepers kept their businesses closed in support of the weekend protest.
The unsanctioned rally came a week after hundreds of people demonstrated in the center of Baku to raise awareness about the deaths of young army conscripts in Azerbaijan.
Twenty-one participants in that gathering were fined on January 14 under a new law against unsanctioned mass demonstrations. The fines ranged from $380 to $760 (300 to 600 manats).
* CORRECTION: This article has been changed to correct an erroneous figure for the dollar equivalence of 250 manats.