Yes, it could be done by the Buddhist monks following the Vinaya rules .
Perhaps one of the best-known training rules of the bhikkhu concerns his not eating between midday and dawn [...]
Fasting in Buddhism is not what most people think, that is, literally surviving without any food, water and sleep for many consecutive days. So the headline must have confused many clueless readers.
Buddhism in Japan
The Japan Times noted that the Buddhist monk, Kogen Kamahori, made an appearance at Enryakuji Temple. The temple belongs to the Tendai school of Buddhism and is also the home of "marathon monks" (a term coined by John Stevens) .
To become a monk there, the candidate (known as gyoja) should successfully complete a 100-day term before trying the 1,000-day term. In the latter, one is required to fast for nine days .
After completing the 700th day, the gyoja faces their most difficult feat. They must survive nine days without food, water, sleep, or rest. This period of time is called the doiri.
In Japan, while some schools of Buddhism follow a particular set of rules in Vinaya, the Tendai priests generally marry and raise families, which is said to be a violation of the rules [1a]. As such, this may lead us to question whether the Japanese monks follow traditional Buddhism or not.
Buddhism and fasting
Fasting in Buddhism has some variations , as quoted below.
[...] In some cases food is only consumed in the morning, before noon, and fasting is practiced from noon until the following morning. In other communities and retreat centers fasting may be practiced for different lengths of time. Often these are water fasts that can last numerous days or even many weeks. [...]
Buddhism is known to practice moderation, which translates to taking less things, including food .
[...] Further, they respect the Buddha's practice of moderation and eat less on those days. The fasting observance is related to several liturgical practices observed on the six fasting days: they recite their precept codes, recite scriptures and increase their hours of meditation on those days.
 The Buddhist Monk's Discipline: Some Points Explained for Laypeople on Accesstoinsight.org, found via [a] this part of article on Wikipedia.
 Kaihōgyō on Wikipedia.
 The Spiritual Athlete's Path to Enlightenment by Holly Schmid.
 Notes on Buddhism and Fasting on howtofast.net.
 A Buddhist Perspective on Fasting on UrbanDharma.org.