In the stage three debate of the Scottish Budget, Ms Forbes estimated that the energy price cap rise of almost £700 "could move a further 211,000 households into fuel poverty, and around 235,000 households who were already fuel poor into extreme fuel poverty".
Announcing financial support measures, she said: "Firstly, we will provide £150 to every household in receipt of council tax reduction in all council tax bands.
"The Council Tax Reduction Scheme already identifies households in greatest need and will allow us to target this intervention.
"Secondly, I will provide local authorities with funding to pass on £150 to other occupied household in Bands A to D in Scotland.
"In total, combining these elements, 1.85m, or 73 per cent of all households, will receive £150 of support."
The £150 payments to support families with the cost of living crisis will either be given as a direct payment by local authorities or used as a credit towards council tax bills, Ms Forbes said.
The Finance Secretary also announced an additional £10m for the Fuel Insecurity Fund "to help households at risk of self-disconnection, or self-rationing their energy use, due to unaffordable fuel costs".
Explaining her decision, Ms Forbes said: "This is clearly an imperfect scheme.
"It will reach some households who may not need this, but it is the only route we have to make sure we reach those for whom it will make a difference, quickly and simply.
"I know that the cost of living crisis is affecting households who are not in receipt of benefits, who are not claiming a council tax reduction. And they are facing hardship too.
"We must seek to do what we can to prevent those households and families on the edge of the poverty line, from falling over it."
Councils will be allowed to carry forward any underspends in funding for Discretionary Housing Payment and the Scottish Welfare Fund into the next financial year.
Moving on to support for businesses, Ms Forbes said that there would be an additional £16m for cultural events that have faced cancellations, £7.5m for Scottish tour operators, £3.5m for outbound travel agents and £3m towards city centre recovery to improve footfall.
One-off grants worth a total of £6.5m will be made available for the childcare sector, including childminders.
She said: "A fully-functioning childcare sector is a pivotal part of our national economic infrastructure."