Colin and Rita Moss, 78 and 79 respectively, were vaccinated at the venue at 10am on Monday.
Rita said: “Colin and I feel really lucky to be getting our vaccines and I’ve never looked forward to getting an injection in my arm, even though I don’t like needles.
“I would definitely encourage others to have their jab when it’s their turn - not just to save themselves but to save others from this horrible virus, too.
“The vaccine is a brilliant thing - it will give us peace of mind and make us feel a lot safer but we won’t be changing what we do or who we see in the short term because we know how important it is to keep following the guidelines until more people have been vaccinated.
“I take my hat off to everyone who has helped us get to this point.”
Dr Jennifer Hill, medical director of operations at Sheffield Teaching Hospitals NHS Foundation Trust, added: “It is tribute to hard work that we have already vaccinated thousands of our most vulnerable residents.
“The arena’s opening is another step forward in rolling out the vaccination programme and it has been fantastic to see people like Rita and Colin getting their vaccinations and being protected against this awful virus.
“We are asking people to help us by not turning up at the arena unless they have an appointment as we cannot vaccinate people ad hoc.
“The teams at the arena, at our hospitals or GP surgeries cannot make appointments for the arena and so by calling or turning up turning up it will simply take time away from the staff who are vaccinating and that is the last thing anyone wants to happen.”