Despite their unpopularity with some climate activists, SUVs made up the majority of all vehicles sold in July.
Medium-sized SUVs were the top-selling vehicle segment, taking 23 per cent of the market.
Compact SUVs had 21 per cent of the market last month and large SUVs had 9 per cent.
In the year to date, the whole market was down 6.6 per cent compared to the first seven months of 2021.
"Registrations of light commercial vehicles remain subdued following the impost of clean car discount taxes from 1 April this year," the MIA said.
The best-selling models in July were the Toyota Hilux (957 units), the Toyota RAV4 (690) and the Mitsubishi Outlander in third place (685).
The association said the Hilux was the best-selling model so far this year, with 5739 units sold.
The Outlander was in second place overall and the Ford Ranger third in the year to date.
Of all carmakers this year, Toyota was leading with 17 per cent of the market, or 15,792 units sold.
Mitsubishi was second with 16 per cent market share, well ahead of third-placed Ford, on 8 per cent.
The MIA said plug-in hybrid registrations in July were steady with 635 units registered last month.
Another 550 new pure electric vehicles were registered, and 1773 petrol hybrids were sold.
