Heavy black smoke rose in Kyiv city centre following the attack, which signalled a new escalation in the conflict.
At least seven people were injured, Kyiv's mayor said.
During more than four-and-a-half years of war with Russia, Ukrainian government buildings have rarely been damaged in drone and missile strikes.
The SBU is vital to Ukraine's war efforts as it executes high-impact, deep strikes to damage Russia's war machine and its energy infrastructure.
"The drone was aimed directly at the office of the Head of the Security Service in that building," Zelenskiy said on the Telegram app.
It was not immediately clear if SBU members were among the injured.
Zelenskiy said that he ordered "an appropriate, tangible response and, where possible, one that mirrors this strike, to the Russians once everything was ready".
Numerous ambulances and emergency services were heading to the scene in the historical part of the city close to the Saint Sophia Cathedral, a UNESCO World Heritage site.
The owner of a popular bakery, Zavertailo, said on the Telegram app that their building located opposite the SBU building was also destroyed in the attack.
One woman shouted into her phone that she had popped out to buy cigarettes and been startled by the explosion.
Ukraine's capital has been under continuous Russian drone attack for 10 days.
On Wednesday, a university in the city centre was also hit.
"I think (people) can get used to this. In the centre of Kyiv, and in the centre of Moscow. It will get worse, I believe this," said Oleh, 33, who declined to give his last name.
The SBU is a vast and secretive agency responsible for ambitious operations against Russia, such as the 2022 bombing of a Russian bridge to occupied Crimea and a 2025 drone attack, codenamed Spiderweb, that struck Russian strategic bombers.
It is also widely seen as a leading player in a campaign of covert assassinations of senior Russian military and other figures blamed by Ukraine for carrying out war crimes.
Russian officials have denounced those killings as terrorist attacks.
Zelenskiy said on Friday US peace negotiators Steve Witkoff and Jared Kushner will visit Ukraine on Sunday after visiting Moscow.
He said Ukraine would guarantee the safety of Russian airspace during the visit of the two to Moscow.
He called on Russia to halt its air attacks on Ukraine during the negotiators' visit to ensure their safety.
US President Donald Trump told reporters on Friday Witkoff and Kushner were heading to Russia and Ukraine to present a proposal to end the war.
with AP
