The king has come under fire for his household's lavish lifestyle while the tiny mountain kingdom's 1.2 million people struggle to make a living.
Mswati reportedly has a personal fortune of around $200 million (152 euros) and the UN estimates that 70 percent of his 1.2 million subjects live below the poverty line.
He has steadfastly resisted reforms.
View gallery."Unmarried Swazi women dance for King Mswati III at …
File picture shows unmarried women from Swaziland dance for Africa's last absolute monarch, King Msw …
The new engagement was announced at a festival which also counted regional delegates who will observe parliamentary elections on Friday.
Critics have slammed the polls as a sham, partly because political parties are banned and candidates are hand-picked by traditional leaders.
The weekend's celebrations were a smaller repeat of last month's official annual Reed Dance, where young virgins from across the kingdom gather and dance for the king.
"It just happened that the international community was there to witness the event," said Mtetwa.
The wedding only takes place once the fiancee falls pregnant. Dlamini will then become Mswati's 14th wife.
The monarch's colourful private life is off-limits in local media, but has drawn a lot of international interest.
Three wives left the household in recent years. The latest, Queen LaGija, fled the palace in 2012 claiming years of physical and emotional abuse.
Another queen, LaDube, was reportedly abused after she was caught in bed with the justice minister, a close friend of the king.
Mswati had kidnapped and married the queen when she was 16 in 2005.
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Topic: Swazi king to wed 14th wife (Read 1726 times)