The attack in the Afghan capital marked unravelling security as the resurgent Taliban continued to pressure Afghan forces, with hundreds of commandos sent to reinforce the provincial capital Lashkar Gah in the south.
Some 36 people were wounded and at least one attacker killed in the Kabul attack, interior ministry spokesman Sediq Sediqqi said.
Special forces had briefly entered the Karte Sakhi shrine near Kabul University to see if any more gunmen were sheltering inside, with police evacuating people from the area, officials said.
Of the 14 killed, 13 were civilians and one a police officer. Three police were among the wounded, Seddiqi said.
“A number of attackers have targeted people in Karte Sakhi shrine,” said Kabul Police chief Abdul Rahman Rahimi.
“Police have evacuated dozens of people from the shrine.” Police also said two grenades had been detonated during the attack
No group has yet claimed responsibility for the assault, which President Ashraf Ghani condemned as a “clear sign of a crime against humanity”.
Ghani vowed the government would use its “maximum capacity” to provide security during Ashura, which will be celebrated on Wednesday.
The threat of attack targeting Shiites was considered particularly serious during Ashura, and many foreign embassies had restricted their staff’s movements until the end of the week in Kabul.
Ashura commemorates the death of Imam Hussein, grandson of the Prophet Muhammad, who was assassinated in 680 and whose tragic end laid the foundation for the faith.
For Shiites around the world, Ashura is a symbol of the struggle against oppression.
The last attack on the Afghan Shiite minority, on July 23 in Kabul, killed 84 people and left 130 injured. It was claimed by the Islamic State organisation.
Tuesday’s attack came as Afghanistan deployed hundreds of commandos backed by NATO air strikes in Lashkar Gah to drive Taliban insurgents from the southern city after their latest attempt to seize the capital of Helmand province.
“More than 300 commandos… have been deployed to the city to prevent Taliban advancement,” said Abdul Jabar Qahraman, government special envoy for security in Helmand.
A NATO spokesman said at least two airstrikes had been carried out in Helmand on Monday defending Afghan troops.
The Taliban have waged an insurgency against the western-backed Kabul government since being toppled from power by a US-led invasion in 2001. They have intensified attacks across the country in recent months, pressuring Afghan forces on multiple fronts.
NATO officially ended its combat mission in December 2014, but US forces were granted greater powers in June to strike at the insurgents as President Barack Obama vowed a more aggressive campaign.
The intervention in Helmand has fuelled the perception that foreign powers are increasingly being drawn back into the conflict.
Around 30,000 people have been displaced in Helmand in recent weeks and most have fled to Lashkar Gah, which is practically besieged by the militants.
In recent months the militants have attempted to overrun other provincial capitals, from Kunduz and Baghlan in the north to Farah in the west, but Afghan forces have managed to repel the attacks.
On Tuesday Taliban fighters renewed their offensive against Farah, triggering heavy fighting that lasted for hours.