The blast ripped through a police van outside the vaccination centre as security officials gathered there to escort polio workers for the third day of a vaccination campaign in Balochistan.
"The blast was apparently carried out by a suicide bomber," Balochistan Home Minister Mir Sarfaraz Bugti told media.
Later, an intelligence official confirmed that it was a suicide attack.
The deceased include 12 policemen, one paramilitary offcier and two civilians, a police official said.
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The Tehreek-i-Taliban Pakistan (TTP) claimed the attack on Facebook and in an email sent to journalists.
Deputy Inspector General (DIG) Police Quetta Syed Imtiaz Shah said seven to eight kilogramme of explosives were used in the blast.
Eyewitnesses at the site said they heard firing after a loud blast rocked the area. The glass windows of nearby buildings shattered due to intensity of the blast.
Police and rescue workers reached the site soon after the blast, while security forces have cordoned off the area.
Today was the third day of a three-day anti-polio campaign which was launched in Quetta and other districts of Balochistan on Monday. The campaign in Quetta was temporarily suspended following the blast.
The campaign was launched to target 2.4 million children under the age of five. Over 55,000 children of Afghan refugees are to be immunised under the campaign.
Polio teams were being dispatched from the polio centre targeted today in the blast, security sources said.
Polio workers have long been targeted in the country by Islamist groups including the Taliban militants which claim that the polio immunisation drive is a front for espionage or a conspiracy to sterilise Muslims.
President Mamnoon Hussain and Prime Minister Nawaz Sharif strongly condemned the blast in Quetta.
In his statement, Sharif said the government is committed to stamp out extremism from the country and operation will continue till elimination of all terrorism.
Balochistan Chief Minister Nawab Sanaullah Zehri also strongly condemed the blast and directed police to submit a report about the incident promptly.