The City of Edinburgh Council said it was unexpectedly left short of 10 drivers. This led to a backlog of refuse due to be collected in some areas.
In a briefing to councillors, it was revealed senior staff with appropriate licences have been drafted in.
The rate of pay for agency staff has also been increased.
Collections will be carried out over the weekend in a bid to clear the backlog.
A City of Edinburgh Council spokeswoman said: "An unexpected shortage of agency drivers has resulted in a reduction in waste collections made in some areas recently - we apologise for any inconvenience caused to residents.
"We have been working with our recruitment agency and will have successfully filled all vacant positions by the beginning of next week.
"In addition, we have temporarily moved some drivers from our cleansing team in the interim.
"We are also carrying out additional weekend collections to reduce the delay."
Supervisors have been drafted in to drive bin lorries in Edinburgh because of a staff shortage.