Researchers say around one in 100,000 people given the jab will suffer idiopathic thrombocytopenic purpura (ITP).
The condition can cause minor bruising around the body and can leave some with a purple-dotted rash.
Almost 350 Brits have been struck down with a separate rare clotting disorder after getting the AstraZeneca vaccine, which was developed by Oxford University.
The complication — blood clots occurring alongside abnormally low platelet levels, cells which cause blockages — spooked health chiefs into advising under-40s are given a different jab.
Edinburgh University experts, who uncovered the link to ITP, did not say how many people also went on to develop clots.
But they said it was likely to be a ‘manifestation’ of the main troubling complication.
Researchers spotted the link after analysing data from 5.4million people in Scotland between December 8 and April 14. By then, 1.7million had received their first dose of the Oxford jab, while 800,000 had the Pfizer-BioNTech vaccine.
They examined vaccinated individuals’ health records to identify any previous issues with ITP, clotting or bleeding disorders and compared these to people who had not been vaccinated.