Police also used tear gas and water cannon against protesters who marched on a military base in Bangkok, calling for King Maha Vajiralongkorn to give up direct command of the army unit housed there.
Protesters threw bottles at police near barricades.
"It was the first time rubber bullets were used," Bangkok police chief Pakapong Pongpetra told reporters on Monday, claiming their use had been necessary to prevent the violence from escalating.
The youth-led political movement is demanding the resignation of Prime Minister Prayuth Chan-ocha, a former junta leader, and has broken taboos by calling for reform of the powerful monarchy.
The Royal Palace has declined to directly comment on the protests.
Police said 22 protesters were arrested on Sunday and charged with violating an emergency decree, enforced since last year to curb the spread of COVID-19, and for obstructing authorities.
Ten protesters and 26 police officers were injured in the clash, Bangkok's Erawan Emergency Medical Centre said in a statement.
A Thai government spokesman said a police officer had also died due to a heart attack.
Prayuth said tougher measures had been employed because protesters initiated violence.
"Police had to use measures according to international standards," he told reporters at the Government House on Monday.
Jutatip Sirikhan, a prominent Thai protester, denied that protesters started the violence.
"The violence only started when authorities cracked down on protesters," she told Reuters.
"Police should be facilitating people's political expression, not firing bullets at them." - Reuters