Niece Gulnaaz Lalji told CBC News that her uncle was having coffee in Nairobi's Westgate mall when the attack began. After a large explosion, Damji went into cardiac arrest and died.
At least 68 people were killed, including Canadian diplomat Annemarie Desloges, in attack by heavily armed militants that began Saturday.
The al-Qaeda-linked group al-Shabaab has claimed responsibility for the attack, which reportedly targeted non-Muslims.
After a prolonged and ongoing stand-off with the militants, who took hostages, Kenya's security forces launched a final offensive Sunday night.