The way global companies identify Crimea has been a highly sensitive issue for both countries since Kremlin-backed forces annexed the region from Ukraine in March 2014.
Ukraine and its Western allies have maintained that this move was illegal.
For users of Apple devices in Crimea, the territory is now shown as part of Russia when it is searched on the U.S. tech giant's Weather or Map apps.
However, those same apps do not show Crimea as part of any country when it is viewed from outside of the region.
The State Duma, Russia's lower house of parliament, said in a statement on the chamber's website on Wednesday that Apple had "fulfilled its obligations and brought the applications on its devices in compliance with the requirements of the Russian legislation."
"Let me explain in your terms, Apple," Ukraine's Foreign Minister Vadym Prystaiko said via Twitter on Wednesday.
"Imagine you're crying out that your design and ideas, years of work and piece of your heart are stolen by your worst enemy but then smb ignorant doesn't give a damn about your pain. That's how it feels when you call Crimea a (Russian) land."
The U.S. and European Union do not recognize Crimea as part of Russia and have imposed sanctions against individuals they believe have violated Ukraine's territorial integrity.
Shortly after the annexation of Crimea just over five years ago, a separate conflict broke out in the eastern Donetsk and Luhansk regions of Ukraine.
Ukraine and its allies have accused Moscow of sending troops to the region and arming separatists. The Kremlin has denied this but says Russian volunteers are helping the fighters.
Former world chess champion Gary Kasparov suggested Apple's decision to change its maps inside Crimea to make it appear as part of Russia constituted "a huge scandal."
"Software is soft power. American tech companies should stand up for the values of innovation that made their success possible, not bow down to dictators for a little extra cash they don't even need. Call Putin's bluff," Kasparov, a long-time critic of the Russian president, said via Twitter on Wednesday.
Last month, Apple was caught in the crosshairs of Chinese state media, when it was criticized for a mapping app in its app store that allowed Hong Kong protesters to track the movement of police.
Apple responded on Friday.
"We would like to clarify for our customers around the world that we have not made any changes to Apple Maps regarding Crimea outside of Russia, where a new law went into effect that required us to update the map within Russia," Apple said.
"We review international law as well as relevant US and other domestic laws before making a determination in labelling on our Maps and make changes if required by law. We are taking a deeper look at how we handle disputed borders in our services and may make changes in the future as a result. Our intention is to make sure our customers can enjoy using Maps and other Apple services, everywhere in the world."