The quake hit just before dawn, causing people to run outdoors in panic.
It struck just as the island is beginning to reopen to tourism as the pandemic wanes.
The US Geological Survey said the magnitude 4.8 quake was centred 62km (38.5 miles) northeast of Singaraja, a Bali port town.
Its shallow depth of 10km (6.2 miles) may have amplified the amount of damage.
A magnitude 4.3 aftershock followed. That quake was relatively deep, at 282km (174 miles).
Gede Darmada, head of the island’s Search and Rescue Agency, said the agency was still collecting updates on damage and casualties. He said the injuries included broken bones and head wounds.
The earthquake triggered landslides in a hilly district, killing at least two people and cutting off access to at least three villages, Darmada said.
It toppled homes and temples in Karangasem, the area closest to the epicentre, killing a three-year-old girl who was hit by falling debris, he said.
“Nearly 60 percent of the houses in our village were damaged and can no longer be lived in,” said I Nengah Kertawa, head of Bunga village in Karangasem, one of the worst-hit communities.
Houses and government facilities also were damaged in Trunyan and in Kintamani, a popular sightseeing destination with a stunning lake.
Bali is home to more than four million mostly Hindu people in the mainly Muslim nation. It is famed for its temples, scenic volcanos and beautiful white-sand beaches.
On Thursday, the island reopened to international travellers for the first time in more than a year after Indonesia’s COVID-19 caseload declined considerably.
The country has had around 1,000 cases a day in the past week after peaking at around 56,000 daily new cases in July.
Indonesia, a vast archipelago of 270 million people, is frequently struck by earthquakes, volcanic eruptions and tsunamis because of its location on the “Ring of Fire”, an arc of volcanoes and fault lines in the Pacific.
The last major earthquake was in January when a magnitude 6.2 earthquake killed at least 105 people and injured nearly 6,500.
More than 92,000 people were displaced after it struck Mamuju and Majene districts in West Sulawesi province.