The shortages are especially bad in the manufacturing sector, according to research by the British Chambers of Commerce and DHL.
Two-thirds of manufacturers are struggling to find suitably skilled staff, and three out of five services firms are also having problems recruiting.
BCC director general Dr Adam Marshall said: “At a time of significant uncertainty and change, it’s pleasing to be able to report that many UK exporters are doing well.
“Yet many tell us that their future prospects are being constrained because it’s becoming harder and harder to recruit the people they need to grow.
“Businesses with global ambitions are facing critical skills gaps at just about every level.
“The combination of decades of constant change in the training system, declines in immigration, and tight local labour markets are stopping many firms from making key investments.
“A stable training system, a reformed apprenticeship levy, answers to practical questions around Brexit and clarity on the UK’s future immigration regime are urgently needed.
“Get these right, and exporters all across the UK will take risks, invest and grow.”
More than 3,300 exporters were surveyed for the study.