However, local media said his condition could be due to exhaustion after a trip to India and other Asian countries in August.
Yosano said Abe had been receiving regular checks from his personal doctor since returning from a regional summit in Australia earlier this week.
"Mr Abe has an illness that could cause him to feel unwell," Yosano said.
"His doctor determined that his fatigue level has reached its peak, so I think that the doctor concluded that he needed to be examined at a well-equipped hospital."
In the wake of Abe's departure, the ruling Liberal Democrat Party has begun moves to select his replacement.
On Thursday Fukushiro Nukaga, the current finance minister, became the first contender to formally throw their hat into the ring.
"I think it is a politician's responsibility and duty to face this difficult time with determination. I want to take the lead," he told party members as he declared his candidacy.
Nukaga, an LDP veteran, has also held the post of defence and economics ministers, but has has twice had to resign over scandals.
Another potential leading candidate is former foreign minister Taro Aso, who is the LDP's secretary-general.
He is expected to announce his candidacy shortly.
Abe's popular predecessor, Junichiro Koizumi, has reportedly refused supporters' pleas to join the race.
But Abe's departure has sparked growing calls for a general election to give Japanese voters a say in choosing the new government.
"With the LDP government thrown into this much confusion, the voters should be asked in the proper fashion who their choice for leader is in a general election," the national Asahi newspaper said in an editorial on Thursday.
"That is the only way to bring back politics based on the people's trust."
The LDP has dominated Japanese politics for more than 50 years, but Al Jazeera correspondent Tony Cheng says that with Abe's departure scandal and incompetence have chipped away at the party's power.
On Thursday LDP officials are expected to approve a plan to choose a successor to Abe by the end of the month, Japanese media said.
|Former foreign minister Taro Aso is thought to |
be a favourite to replace Abe [EPA]
Until then, Abe will stay as caretaker - although how that might be affected with him in hospital is not clear.
Other names floated for Abe's successor include former finance minister Sadakazu Tanigaki, former chief cabinet secretary Yasuo Fukuda, as well as party heavyweight Taku Yamasaki.
Abe's sudden decision to quit came less than a year in power amid a string of scandals that scuttled his plans to raise Japan's global security profile, sending his approval ratings plummeting.
The wave of scandals since late last year cost him five cabinet ministers, including one who committed suicide, and sparked public anger over the mismanagement of pension records.
The LDP's heavy defeat in July's upper house elections also put Abe under intense pressure.
Adding to his woes were questions over a plan to extend Japan's naval mission supporting the US-led war in Afghanistan, which Abe cited as the primary reason for quitting the post.