The protesters, marching on Banthad Thong Road, were demanding the resignation of the government of Prime Minister Yingluck Shinawatra, the Bangkok Nation reported.
The injured people, several seen covered in blood, were taken to various hospitals in the Thai capital, the report said.
The protesters, who have been waging their campaign since November, have closed some sections of the capital as part of their new "Bangkok shutdown" campaign.
At least eight people have died since the protests began.
The Nation said injured protesters were seen on Bluesky satellite television that aired the incident live.
Security officers of the protest movement's People's Democratic Reform Committee were quoted as saying the explosive device was lobbed from a three-story abandoned building.
The report said the number of the protesters has decreased this week.
Gen. Paradon Pattanathabut, national security chief, estimated about 12,000 people were on the streets Friday, a fraction of the estimated 170,000 people who had assembled Monday. Demonstrators said the numbers are far higher than official estimates.
On Tuesday, two protesters were injured in a shooting incident and an explosive device was thrown at the home of Thailand's opposition leader, but no one was hurt in that attack..
Yingluck said Friday the best way to remove her from office would be to vote in the Feb. 2 general election, but the main opposition Democrat Party and the protesting PDRC have boycotted the election.
"I'm here because (of) my duty as caretaker prime minister until new government is elected. Cannot say I just step down. Using vote in election is the best way," Yingluck said.
On Wednesday, Yingluck announced the election would go on as scheduled. The protesters oppose the election being overseen by Yingluck's government, demanding that it be conducted by a "people's council."
Yingluck's opponents maintain her government is corrupt and is controlled by her brother Thaksin -- a former premier and a telecommunications billionaire who has lived in exile since he was ousted in a coup in 2006. The government denies the allegations.