Hundreds of protesters chanting "Shame!" and "No to Russification!" were blocked from entering the building.
The Kharkiv City Council voted to implement the new law on state-language policy.
President Viktor Yanukovych earlier this month signed the law, which clears the way for an increase in the use of Russian in regions of Ukraine where Russian is spoken by most people.
The move has angered many Ukrainians, who view the law as weakening Ukraine's sovereignty in an attempt to curry favor with Moscow.