The Centre for Health Protection is investigating three related cases of spotted fever, involving three men who hiked in Tai Lam Country Park on October 18 and 19.
They are aged 15 to 46. They developed a fever, rash and skin ulcers from late October to early November.
They have all received treatment in hospital and have been discharged.
They all tested positive for spotted fever, and the centre is contacting 20 other hikers who were with them in the park.
Spotted fever is transmitted by ticks, which are usually found in scrubby areas or on rodents and stray animals.
Hikers are advised to wear long sleeves and pants, and use DEET-containing insect repellent. They should also avoid walking through vegetation or feeding wild or stray animals.