International deks: Mr Arestovych apologised and said he had made a “fundamental error”.
The original remark caused widespread anger in the country, and was used by Russian officials to blame Ukraine.
The adviser is a well-known figure because of his daily updates on YouTube, watched by millions.
Ukraine’s President Volodymyr Zelensky has not yet commented on Mr Arestovych’s decision to resign.
Hours after Saturday’s missile strike hit an apartment building in Dnipro, Mr Arestovych initially said it appeared that the Russian missile had fallen on the building after it was shot down by Ukrainian air defences.
Ukraine said the building was hit by a Russian Kh-22 missile, which it does not have the capability to shoot down and is reportedly extremely inaccurate.
Ukrainians reacted angrily to Mr Arestovych’s initial comments, with some accusing him of strengthening the position of Russian propagandists. Some Ukrainian parliamentarians signed a petition calling for Mr Arestovych to be dismissed as a government official.
He later posted a letter tending his resignation and said he had made a “fundamental error”.