Security forces patrolled throughout the night in the capital Mbabane and the city of Manzini 40 kilometres (25 miles) away as helicopters flew constantly overhead, local residents said.
Many stores were shuttered and the streets were virtually empty, while public transport was at a standstill, AFP reporters saw.
Witnesses said some streets in outlying districts had been barricaded and they had seen burning tires, after campaign groups called for a commemoration of the anniversary.
Demonstrations in the southern African monarchy broke out on June 29, 2021, led by young people clamouring for democratic reform.
Eight people died in clashes with the security forces, initiating protests over the following months that have since become sporadic.
According to the authorities, 37 people have died, while Human Rights Watch (HRW) puts the toll at 46.
Eswatini, previously known as Swaziland, is Africa's last absolute monarchy.
King Mswati III, who ascended to the throne in 1986 at the age of 18, appoints ministers and controls parliament under a convoluted electoral system. Political parties have been banned for nearly half a century.
Mswati has been widely criticised for his lifestyle, reputedly lavishing his 15 wives with millions of dollars a year while nearly 60 percent of the population of 1.2 million live on less than $1.90 a day.