The cases have fuelled fears about the effectiveness of potential vaccines against the virus, as it would appear that immunity only lasts a short period of time. However, experts have warned against reading too much into isolated cases - in a pandemic that has infected more than 23 million people.
Harris told the BBC that extensive testing in Hong Kong showed reinfection was still likely to be fairly uncommon.
"We would expect that given the quality of the surveillance - and the study in Hong Kong shows what a high level of surveillance they are doing there - you would have expected to see many more cases if this was happening a lot," she said.
Harris told the BBC: "What's important here is this is just one case out of more than 23 million, so while we did expect that it could happen it is not clear that this is something that is likely to happen to many people."
"But what it also tells us is what we long suspected, that we don't know enough about how long immunity lasts or whether it lasts a long time in most people or many people, or not many people so all of those questions are still open."
Harris said the news did not provide any indication of a potential second spike in coronavirus cases, but said that "this idea that many people had was like 'just let it wash over us, it will be fine', was never a wise choice."
Virologist Dr Marc Van Ranst said the Belgian case was a woman who had contracted Covid-19 for the first time in March and then again in June. Further cases of re-infection were likely to surface, he said.
"We don't know if there will be a large number. I think probably not, but we will have to see," he told Reuters.
Previous antibody studies have shown that immunity wanes over the time, raising questions about the effectiveness of any future vaccine. The team behind the Oxford University vaccine - touted as the front-runner - have already said that any immunisation may have to be given annually, like the flu jab.
Van Ranst agreed. "Perhaps a vaccine will need to be repeated every year, or within two or three years. It seems clear though that we won't have something that works for, say, 10 years," he said.
Van Ranst said in cases such as the Belgian woman's where symptoms were relatively mild, the body may not have created enough antibodies to prevent a re-infection, although they might have helped limit the sickness.
In the Hong Kong case, the reinfected person did not have any symptoms the second time and the infection was picked up through airport screening. Researchers said this may indicate that previous exposure to the virus may mean that subsequent infections are milder.
The National Institute for Public Health in the Netherlands has also announced it had also observed a Dutch case of re-infection.
Virologist Dr Marion Koopmans was quoted by Dutch broadcaster NOS as saying the patient was an older person with a weakened immune system.
She said cases where people have been sick with the virus a long time and it then flares up again were better known. Previous cases of reinfection have been put down to the virus lingering in the body for a long time or false negative tests.
Koopmans, an adviser to the Dutch Government, said re-infections had been expected.
"That someone would pop up with a re-infection, it doesn't make me nervous," she said. "We have to see whether it happens often."
