"A tsunami has happened in Palu", said Rahmat Triyono, head of the agency's natural disaster and tsunami division, referring to the city of 350,000 almost 80km from the quake's epicentre.
Indonesia's seismological agency BMKG put the magnitude at 7.4.
A house sits damaged after the natural disaster in Donggala, central Sulawesi, Indonesia.
The tsunami was caused by a 7.5 magnitude quake which hit just off central Sulawesi last night.
The authorities had warned people to take cover after issuing natural disaster alerts.
Dramatic video footage filmed from the top floor of a parking ramp in Palu, almost 80 kilometers (50 miles) from the quake's epicenter, showed waves of water bring down several buildings and inundate a large mosque.
"There are reports that many buildings collapsed in the natural disaster", Nugroho said in a statement.
He said families were reported missing and communications and power supplies were disrupted.
Waves of up to 2m (6.6ft) high swept through Palu on Sulawesi island, not long after authorities had lifted a tsunami warning.
Bill Cosby Possibly Headed to Jail on Monday
Defense attorneys would be allowed to cross-examine witnesses, said Kate Delano, spokeswoman for the county prosecutor's officer. Lublin said she thinks "it's important that he spend some time behind bars". "I feel like my faith in humanity is restored".
Officials asked people to remain alert as a number of moderate aftershocks hit.
BNPB spokesman Sutopo Purwo Nugroho shared a video on Twitter of the tsunami striking the coast at Palu.
Amateur footage of the tsunami has gone viral on social media and has been shown on local TV stations. In 2004, the Indian Ocean tsunami killed 226,000 people in 13 countries, including more than 120,000 in Indonesia.
It followed a fatal 6.1 magnitude quake earlier Friday, which left one person dead and at least 10 people injured.
In Palu, a large bridge which was a symbol of the city was completely destroyed.
AFP phone calls to several regional hospitals went unanswered and Palu's main airport was closed around 7.30 pm local time, with authorities saying it would not open for 24 hours.
Almost 400 people were killed when a powerful quake sent a tsunami barrelling into the Indonesian island of Sulawesi, officials said Saturday, as hospitals struggled to cope with hundreds of injured and rescuers scrambled to reach the stricken region.
"All the things in my house were swaying", another Donggala resident, Mohammad Fikri, said of the earlier 6.1 quake.