Russia has warned Ukraine that relations between the two countries will be harmed if it joins Nato.
Anti-US sentiment has been running high among protesters
MPs in the State Duma voted 435 to 0, with one abstention, for a resolution expressing "serious concern" over Ukrainian plans to join the alliance.
The message was sent as the parliament in Kiev was to have a vote - now delayed - on allowing in foreign troops ahead of joint manoeuvres with the US.
Nato has called on Ukraine to avoid politicising the exercise next month.
The joint exercises involving a number of Nato countries are due to start on 12 June in Crimea and 200 US marines have already arrived to help prepare facilities.
A Nato spokesman said the exercises were routine, but not organised by Nato.
"These are bilateral exercises between the US and Ukraine open to Nato allies and partners, but not organised by Nato or funded by Nato," James Appathurai told the AFP news agency.
The Ukrainian deputy chief of staff, Rear Admiral Ihor Knyaz, has said Russia itself has been invited to participate.
Pro-Russian demonstrators have picketed a US warship taking part.
The Ukrainian parliament postponed the vote on allowing in foreign troops until 14 June.
Pro-Western President Viktor Yushchenko, who has made joining Nato a top priority, had asked parliament to urgently grant permission for foreign troops to be on Ukrainian soil.
But co-operation has been difficult since MPs have been unable to form a coalition following a parliamentary election in March.
The BBC's Helen Fawkes, in Kiev, says that if the military exercises have to be cancelled because of the delay, it will be seen as a humiliating blow to the pro-Western authorities.
Mr Yushchenko's enthusiasm for joining Nato has angered many in the mainly Russian-speaking areas of Ukraine, like Crimea, who are opposed to the former Soviet republic joining the alliance.
For almost two weeks, there have been anti-Nato protests in the region, which is home to the Russian Black Sea Fleet, and hostility towards the Nato alliance is especially strong.
On Tuesday, the regional parliament declared Crimea a Nato-free zone. This was dismissed as meaningless by Ukraine's president.
Pro-Russian political parties have backed the protests.
And Russia's State Duma seemed clear in its message to Ukraine's parliament on Wednesday.
"Ukraine's membership in the military bloc would have negative consequences for the entire range of relations between our two fraternal peoples," the Russian deputies said.
They expressed similar concern about Georgia joining the alliance.
"We have said more than once that every country has the right to take sovereign decisions on who will be its partner in the international arena," Foreign Minister Sergei Lavrov told the State Duma before the vote.
"At the same time, the acceptance into Nato of Ukraine and Georgia will mean a colossal geopolitical shift and we assess such steps from the point of view of our interests."