AMs on the public accounts committee heard they could be worth millions of pounds, but it depended on the progress of police investigations.
Committee chair Darren Millar said: "I am alarmed that we have seen such a significant increase."
Top civil servant Sir Derek Jones said 18 was only 0.3% of the organisations funded, but it was "clearly worrying".
Sir Derek, the Welsh government's most senior civil servant, added that it was "very problematic when it happens".
Few details were given to the committee, other than that the cases were mainly in one area of business and one part of Wales.
"It's not a huge problem, but we are dealing with them," he said
Extra resources have been put into the counter-fraud unit to deal with the pressure as a result of the complexity of the investigations, Sir Derek said.
Sir Derek also told the committee:
The number of suspected fraud cases against the Welsh government has doubled in the past year, from 9 to 18.