The motion, passed on Thursday evening, also urged the Russian authorities to immediately release Navalny, President Vladimir Putin's most prominent critic.
Navalny was detained last weekend and then jailed for alleged parole violations after flying back to Russia for the first time since being poisoned by a military-grade nerve agent. He accuses Putin of ordering his murder, which the Kremlin denies.
The Reuters news agency reported that, responding to Navalny's arrest, European Union lawmakers in Brussels on Thursday called for the bloc to stop the completion of the contested Nord Stream 2 gas pipeline from Russia to Germany.
The resolution is not binding but ramps up political pressure on EU member states, according to public broadcaster Polish Radio's IAR news agency.
Poland's president and prime minister called for the release of Navalny earlier this week.
Meanwhile, a deputy foreign minister in Warsaw said on Monday that Poland had started talks with other EU countries in a push for an urgent debate by the UN Human Rights Council on Navalny’s arrest.