Letters are now being sent out to more than 37,800 customers warning them of the theft and advising them what action to take.
Those affected include people receiving winter fuel payments, people in receipt of care grants and council suppliers.
The information, which includes names and addresses, relates to 17,692 companies and 20,143 individuals.
It includes bank account details of 10,382 firms and 6069 individuals.
The laptop was one of two stolen during a break-in at the council offices in Cochrane Street, Glasgow, between Monday May 28 and Tuesday May 29.
But the full extent of the data loss did not become apparent until Wednesday June 6. The laptop was not encrypted but was password protected. No personal data was stored on the second laptop.
The council has informed the Information Commissioner and Strathclyde Police and will be contacting customers' banks where appropriate.
Staff from the council's internal audit section are also carrying out a full investigation.
A spokesman said: "We are writing to the people affected by this theft to alert them to the data loss and offer them advice."
Affected customers who have any questions can contact the city council on 0141 287 0400 between 9am and 5pm, Monday to Friday.