The 18-year-old - who is classed as being in a vulnerable group - received his first dose on Friday, and Price previously reassured followers he was safe and well despite suffering side effects.
But Harvey has written to say thank you to all the doctors and nurses for looking after him and “doing a good job with my injection”.
Watch: Katie Price lands documentary on becoming a paramedic
He wrote: “Dear NHS doctors and nurses. I am writing to say well done for looking after Harvey and everybody and doing a good job with my injection on Friday.
“You are all proud of me. You work hard everyday. We all need a holiday. I will send you more pictures to keep you happy and safe.
''Thank you and well done. Love from Harvey Price.”
Price, 42, captioned the picture of the note: “Can’t resist showing you this - what @officialmrharveyprice has written today with no help ... it amazes me everyday what must go through Harvey’s mind.”
Price previously revealed in a video on Instagram that Harvey - who takes a variety of medications for autism, ADHD and Prader-Willi syndrome - was taken to hospital, just hours after receiving his first dose of the Oxford/AstraZeneca coronavirus vaccine.
Harvey began to feel unwell and had a high temperature of 39.9 degrees on Friday evening, in the wake of having the injection, and was taken to A&E for tests.
But she has urged people to get a COVID jab, saying she is much happier knowing her son has been vaccinated against the virus.
She said: “I don't want anyone worrying about him as he’s fine now at home eating carrot cake. Despite Harvey's reaction, he is one of a kind, the COVID jab is so important especially for those in high risk categories.
"I am so much happier in the knowledge Harvey is safer now he has had his."
Harvey - who recently appeared alongside his mother in BBC documentary Katie Price: Harvey & Me - was taken to hospital last July after suffering chest pains, and was treated in intensive care.
Mother-of-five Price had first child Harvey following a brief relationship retired footballer Dwight Yorke, 49, but he initially denied he was his father and demanded a paternity test.
Watch: Katie Price reassures people about the coronavirus vaccine