King Abdullah, who took power in 2005 after the death of his half-brother King Fahd, is thought to be 91, although official accounts are unclear. He has undergone surgery in the past few years related to a herniated disc.
Saudi stocks dipped on the news, which will also be of wider interest as Saudi Arabia is the world's largest oil exporter and the top U.S. ally in the Gulf region. Global oil prices did not appear to be immediately affected.
"The Custodian of the Two Holy Mosques, King Abdullah bin Abdulaziz, may God keep him, entered today, Wednesday, ... the King Abdulaziz Medical City of the National Guard in Riyadh to undergo some medical tests," the statement said, according to state news agency SPA.
A Saudi source familiar with the affairs of the royal family said the king suffered breathing difficulties and was transferred to hospital. "But he's feeling better now and he is in stable condition," the source told Reuters.
Saudi Arabia's stock market, which was already down more than 1 per cent due to sliding oil prices, dropped to 5 per cent lower in the minutes after the news. It later recovered slightly to be 3 per cent lower.
Abdullah named his half-brother, Prince Salman, 13 years his junior, heir apparent in June 2012 after the death of Crown Prince Nayef bin Abdulaziz. Earlier this year, he appointed Prince Muqrin bin Abdulaziz as deputy crown prince, giving some assurance on the kingdom's long-term succession process.
In November 2012, the king underwent an 11-hour operation at the same Riyadh hospital. He had a similar operation in October 2011 and had back surgery twice in the United States in 2010 for a herniated disc, spending three months outside Saudi Arabia recuperating.