Nemtsov, 55, who served as first deputy prime minister in the 1990s, was fatally shot from a passing car near the Kremlin late Friday.
As the leader of the opposition Republican Party of Russia-People’s Freedom Party, he was one of the most outspoken critics of President Vladimir Putin and Russia's role in the Ukraine conflict.
"The Secretary-General notes that an investigation into this murder has been announced, and he expects the perpetrators to be brought to justice swiftly," according to a statement issued from Ban's office.
Putin said on Saturday that he would do everything possible to bring to justice those responsible for the murder.
According to Russian media, the opposition leader had received many death threats in the past, which he shared with Russian security officials.