The variant, known as BA.2, has spread widely in countries such as Denmark, and so far 26 cases have been recorded in Scotland.
Asked how serious the development is, Professor Leitch told Thursday’s Covid-19 recovery committee that he is “mildly" concerned.
It appears the sub-variant may be more transmissible, but not more severe, Prof Leitch said.
“It appears in the early research to have one advantage,” he said.
“It's tricky to be sure in the early stages, but what we call the secondary attack rate, which is the number of people who get it when a positive arrives, particularly in a household for example, appears to be slightly higher with BA.2 than it was with BA.1, which is the original Omicron.
“[It’s] 29 per cent versus 39 per cent, so in rough terms, 40 per cent of people in a household get BA.2 if somebody has it, and 30 per cent get BA.1 if somebody has it.
“It's not a huge difference, but it would appear that it has a slight advantage.
“In Denmark BA.2 is now crossing over BA.1 and taking over, and we expect to see that probably around the rest of the world.”
Prof Leitch added: “The good news is that it doesn't cause more severe disease. You may be slightly more likely to catch it, particularly if you are unboosted, but you won’t end up sicker.
“Remember milder disease is not mild, it can still be very very bad, but we shouldn't be overly concerned about it.”
He said: “For now the fundamental answer is ‘mildly worried’. We are monitoring around the world, but there is no more severe disease as yet.”
In an update to MSPs on Tuesday, Ms Sturgeon said 26 cases of BA.2 have been confirmed in Scotland, but this was likely to be an underestimate.
"Investigations into this are ongoing, both in the UK and in other countries, such as Denmark, where the sub-variant has been circulating for longer,” she said.