NHS Lothian said the vaccine was eventually delivered around lunchtime and all those affected had been given new appointments to make sure they get their jags.
But Edinburgh Southern Labour MSP Daniel Johnson called for more information on vaccinations to be made available.
He said he had written to health chiefs asking how many healthcare staff had been vaccinated, what the forward programme was and what the situation with supplies was.
“Whether it’s frontline staff or whether it’s older and vulnerable people, we keep having these cancellations and without clear explanations about what's going on. Given the sensitivity of everything just now, we just need clearer information.
"I think the health board need to provide a weekly update on how vaccination is progressing, just so we know how it’s going – they need to provide more information. If they don’t get better at telling us what’s going on, it’s going to lead to unhelpful speculation.”
Lothian Tory MSP Miles Briggs said there were growing questions about the roll-out of the vaccine. “NHS Lothian is going to have to explain what this delay was. Yes people have appointments rearranged, but we should really be powering through to get NHS staff vaccinated as soon as possible and this is time which has not been properly used.”
And Edinburgh Western Lib Dem MSP Alex Cole-Hamilton said: “The vaccine is our route out of the pandemic and all government attention should be focused on getting it to people as quickly as possible.
“We know they are sitting on a stockpile of over 200,000 Scottish doses somewhere in England and yet we’re seeing health boards like Lothian run dry just at a time when we should be offering protection to our heroes on the frontline.”
David Small, director of primary care transformation and Covid vaccination project lead at NHS Lothian, said: “Unfortunately, there was delay this morning which caused a vaccine delivery not to arrive on time for morning appointments in Astley Ainslie Hospital. The issue has now been rectified and those staff members who did not get their vaccine this morning as planned have been given new appointments.”