"For security reasons, Parc de la Ciutadella is closed to the public today," Catalonia's regional police force, the Mossos d'Esquadra, said in a Twitter message.
The goal is to "prevent any situation that would put pressure on parliamentary activity", a police spokesman said.
During a massive rally in Barcelona on Sunday against independence "a group of people forced their way into the park and threw objects against the parliament building," he added.
"We are trying to avoid these situations, both on the part of pro-unity protesters as well as by groups of radical separatists," the spokesman said.
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During a protest held in July 2011 against austerity measures, demonstrators surrounded the parliament building, a former military arsenal, and several regional lawmakers were harassed as they tried to enter.
The head of the regional Catalan government at the time, Artur Mas, was forced to enter the building by helicopter.
Catalonia's main separatist organisations had called for supporters of Catalan independence to gather in front of the parliament "to support and defend the declaration of independence."
They will now gather outside of the park instead.
Final results from the vote suggest 43 percent of Catalan voters turned out and 90 percent of them backed independence -- but "No" voters largely boycotted the ballot.
Separatists hope Puigdemont will use his address to unilaterally declare independence for Catalonia, a region of 7.5 million people that is about the size of Belgium.
But Spanish Prime Minister Mariano Rajoy's conservative government has vowed to block any independence declaration.
It has several tools it can use, including suspending Catalonia's regional autonomy or declaring a state of emergency.