The Atlantic alliance echoed the European Union's earlier condemnation of the bridge, which Russian President Vladimir Putin drove a truck over on Tuesday.
"NATO condemns Russia's construction and partial opening of the Kerch Strait bridge between Russia and Crimea," NATO deputy spokesman Piers Cazalet said.
"Crimea is part of Ukraine and this bridge represents another violation of Ukraine's sovereignty and territorial integrity," Cazalet said in a statement.
The bridge, which limits sea traffic to Ukrainian ports on the Azov Sea, amounts to "the infringement of its navigational rights in its territorial waters," he added.
"Russia continues to demonstrate a clear disregard for international law," Cazalet said, adding that NATO will not recognise Russia's 2014 annexation of Crimea.
Russian state television showed Putin dressed in jeans and a casual jacket sitting behind the wheel of a construction truck to drive across the bridge and officially open it.
The 29-member NATO is pursuing a dual-track policy towards the Kremlin of defence and deterrence coupled with an offer of dialogue.
Tensions between NATO and Russia are at levels not seen since the Cold War, including over Moscow's support for pro-Russian separatists in the conflict in eastern Ukraine.
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