According to state reports, the patient from Bayannur city - a herdsman - is in quarantine and in a stable condition.
It is not yet clear how or why the patient might have become infected.
Officials issued a Level 3 warning, the second-lowest in a four-tier system. The level 3 alert forbids the hunting and eating of animals that could carry plague and calls on the public to report suspected cases.
The bubonic plague, caused by bacterial infection, can be deadly, but can be treated with commonly available antibiotics.
Cases of bubonic plague are periodically reported around the world.
Madagascar saw more than 300 cases during an outbreak in 2017. In May last year, two people in the country of Mongolia died from the plague, which they contracted after eating the raw meat of a marmot - a type of rodent.
The bubonic plague is characterised by swollen lymph nodes. It can be hard to identify in its early stages because symptoms, which usually develop after three to seven days, are flu-like.
But it's unlikely the bubonic plague - infamously known as the Black Death - will lead to an epidemic.
"Unlike in the 14th Century, we now have an understanding of how this disease is transmitted," Dr Shanti Kappagoda, an infectious diseases doctor at Stanford Health Care, told news site Healthline.
"We know how to prevent it. We are also able to treat patients who are infected with effective antibiotics."
The Black Death caused about 50 million deaths across Africa, Asia and Europe in the 14th Century.
Its last terrifying outbreak in London was the Great Plague of 1665, which killed about a fifth of the city's inhabitants. In the 19th Century there was a plague outbreak in China and India, which killed more than 12 million.