But she has not been seen in public since March 28, according to South Korea's Yonhap news agency, sparking fresh rumours about her.
Toshimitsu Shigemura, a professor at Tokyo's Waseda University and an expert on North Korea, told the Daily Telegraph: "There are several possible reasons, including that she is pregnant or that there is some sort of problem between the two of them."
A former member of the North's Unhasu Orchestra, there have been stories before about Ri being pregnant, and even having a child.
In 2013 former US basketball star Dennis Rodman, who has referred to Kim as a "friend for life", said they had a baby daughter called Ju-ae.
He said: "I held their baby Ju-ae and spoke with Ri as well. He's a good dad and has a beautiful family."
But it is not thought that a daughter would be an acceptable heir, hence the rumours that she may be pregnant again, possibly with a son.
But Mr Shigemura said another rumour was that she may have fallen out with his powerful younger sister, Kim Yo-Jong.
"The belief is that while Mr Kim lacks political ability, she is far more adept at the sort of manoeuvring that is required to keep him in power, so that is the task she has taken on," Mr Shigemura said.
Ri was pictured wearing stylish, expensive-looking outfits and on one occasion sported what appeared to be a Christian Dior handbag, in a country plagued by chronic poverty.
The Kim dynasty has ruled the isolated state for nearly seven decades with an iron fist and pervasive personality cult.
Kim Il-Sung led North Korea from its establishment in 1948 until his death on July 8, 1994.
He was succeeded by his son, Kim Jong-Il, who also ruled until his death in December 2011 when power was transferred to his son and current leader Kim Jong-Un.
KCNA said "an endless stream of people" was visiting, Mangyongdae, the birthplace of Kim Il-Sung, as the Day of the Sun draws near.