Qaboos, 79, believed to be suffering from colon cancer, has rarely appeared in public since undergoing lengthy treatment in Germany in March 2015.
The statement said the checkup will take “a limited period of time”, but did not specify the duration or give details on his condition.
The sultan’s ill health and repeated hospital spells in Germany have focused attention on the fact that he has no designated successor.
Qaboos, who has ruled the Gulf sultanate since 1970, is unmarried and has no children or brothers.
According to the constitution, the sultan must write a letter designating a successor from the ruling dynasty, to be opened in the event that his family cannot agree on his replacement within three days of his death.
The sultanate’s Basic Law says the royal family should choose a new sultan within three days of the position falling vacant.
Should it fail to reach an agreement, the nation’s defence council, the head of the Supreme Court and the heads of the two chambers of the consultative council would then enforce Qaboos’s choice and enthrone the person he designated in the envelope.