While it was not immediately clear who was behind the blast, Thailand has a long history of bomb attacks on symbolic dates.
The small device -- which police said was potentially deadly -- went off near the VIP section of King Mongkut hospital as patients and their families waited for prescriptions, shattering glass and sending smoke into the corridors.
Hospital director Saroj Keokajee said the "low intensity bomb" injured 21 people, among them retired military officers.
"Eight people were admitted to hospital to observe their condition... among them is one woman who needed surgery because of shrapnel buried in her jaw," he said.
Thailand has remained starkly divided since the May 22, 2014 coup, but dissent has broadly been smothered by a military with sweeping security powers.
While it was not immediately clear who was behind the blast, Thailand has a long history of bomb attacks on symbolic dates -- carried out by militant political factions or separatists linked to an insurgency in the Muslim-majority south.
Investigators said the bomb may be linked to two other similarly small devices that went off in recent weeks, one outside Bangkok's National Theatre a week ago and another left in a Bangkok bin in early April.
Both were too low yield to cause significant injury. But police said Monday's device, while similar in size, was more serious because it was packed with nails.
"The people who did this are brutal," national police chief Chakthip Chaijinda, told reporters. "If they (the nails) had directly impacted, they could cause death."
The clinic in central Bangkok is often used by serving and retired members of the armed forces but also treats civilians.
Saroj said no senior military officers were near the blast.
Regardless of the motive, the blast will raise the political temperature in Thailand where violence had declined under the military's stranglehold.
Despite a veneer of stability Thais remain divided and uncertain over the future three years after the ousting of the elected government of Yingluck Shinawatra.
Protest and political gatherings are banned while dissidents have been rounded up on charges of sedition or breaching junta orders, or under draconian royal defamation legislation.
Militant elements among pro-democracy groups have either been arrested or gone to ground.
The one region where daily violence and large bomb blasts persist is the country's "Deep South", where Malay Muslim militants have fought a long insurgency.
But they rarely strike outside their region -- an exception being in August 2016 when a series of coordinated blasts hit a string of tourist towns.
The country's notoriously fractious domestic politics have incubated the worst violence.
Over the past 10 years Thais have witnessed repeated rounds of deadly protests, a string of short-lived governments and two military coups that deposed elected leaders.
The junta says its 2014 coup -- the 12th time generals have successfully seized power -- was needed to bring stability and root out corruption.
But critics say the military is deeply hostile to ousted premiers Thaksin Shinawatra and his sister Yingluck, whose parties have won every poll since 2001.
Their billionaire clan is popular among Thailand's rural and urban poor and they have urged a return to elections.
But the Shinawatras are hated by Bangkok's military-backed elite, who accuse the family of corruption and nepotism.
In a statement on Facebook to mark the coup Yingluck decried a lack of "concrete reform" and warned that three years of military rule risked becoming a "waste of time".