Ms Sturgeon told MSPs the extra money from the Scottish Government would allow many more people access to crisis grants, for which demand is expected to grow.
She announced the £33million Scottish Welfare Fund at the SNP Conference in Perth at the weekend. It will replace the old Social Fund, with the Scottish Government adding £9m to £23.9m being transferred from the UK Department of Work and Pensions.
She has now told the Scottish Parliament Welfare Reform Committee the fund will mean an additional 5000 community care grants and 100,000 crisis grants will be available to people who need urgent assistance or a one-off small grant.
Ms Sturgeon said: "It will almost double the number of people in Scotland able to get a community care grant or crisis grant next year.
Labour MSP Iain Gray said many people were currently being refused because they were told there were no funds left and there were no appeal grounds. He asked if this could be addressed.
Ms Sturgeon said details had still to be finalised and the Scottish Government would look at the possibility of appeals.
She added: "It is a cash limited fund, but it will be bigger than any time in the last seven years.
"We understand demand for a fund like this is likely to be rising."
It is understood officials believe it is possible the Welfare Fund could still run out of cash but that it would be significantly later in the year than previously.
They also say many more people will have access to the emergency funds.
Last year the Fund had £29m available to distribute, with £20m for community care grants and £9m for crisis grants. An extra £9m is being put in next year.
Concerns were also raised about the introduction of the new Universal Credit scheme, which will replace many different benefits with single payments.
The change is due to take effect next October, but Ms Sturgeon said the Scottish Government had not been able to finalise how it would apply in Scotland because it was still waiting for full details from Westminster.
However, she said she could give a reassurance the intention was to continue access for people who currently are eligible.