Local residents were targetted in four parts of the town by the elite Republican Guard and special police units. They launched appeals for help but were unable to get the victims to safety, the source said.
The attacks continued into the night, he added, without giving any information on what sparked the bombardment.
Taez, 270 kilometres (170 miles) southwest of Saana, is one of the main focuses of the protest movement against the regime of President Ali Abdullah Saleh.
Earlier Tuesday, shells fired into a popular shopping district of Yemen's capital killed two civilians as demonstrators called for the president to be put on trial.
Tens of thousands of people marched in Sanaa Tuesday calling for Saleh's ouster and trial.
Saleh, in power for 33 years, has so far refused to resign despite the wave of popular protests that has swept the country since January demanding that he step down.
The UN envoy to Yemen, Jamal Benomar, who arrived in the country last month to try to resolve the deteriorating political crisis, left Sanaa on Monday without managing to broker a solution.