Police roadblocks have also been mounted around the city.
One unconfirmed report circulating on social networks says three leaders of the Swaziland National Association of Teachers (SNAT), one of the trade unions leading the protests, have been taken into custody by security forces.
The protests are to mark the anniversary in 1973 when King Sobhuza II tore up the constitution and began to rule by decree.
His son, King Mswati III, the last absolute monarch in sub-Saharan Africa, presently rules the kingdom where all political parties are banned.
Protestors are calling for democratic reforms.
ACTIVISTS READY TO FIGHT ON THE STREETS