The drop in exports to the US came after the Trump administration announced new 25% tariffs on cars and car parts in March.
This “depressed demand instantly forcing many manufacturers to stop shipments”, the SMMT said.
Jaguar Land Rover (JLR) suspended shipments to the US in April, while Aston Martin reduced exports, after the tariffs were imposed early in the month.
The US share of UK exports fell from nearly a fifth to just over a tenth in May.
Production was also hit by continuing work to change factories over to electric vehicle production, the SMMT said.
For example, JLR is shifting Jaguar to being an all-electric brand, and Nissan is preparing for a new Leaf model.