"Johnny is physically fine. There are some issues with a family member, some health issues, that he's tending to," Price said.
Cueto, who is likely to be Cincinnati's Opening Day starter, is back home in the Dominican Republic. Price expected the right-hander's throwing program to remain on schedule.
"He is able to utilize the complex [in the Dominican Republic] to continue to throw, throw bullpens and things of that nature," Price said.
Cueto, 29, has a 3.00 ERA through three spring starts with five hits, four walks and one homer allowed through nine innings with six strikeouts. Last season, he was the National League Cy Young Award runner-up after he went 20-9 with 2.25 ERA.
In Spring Training, there is no bereavement list for players to be placed for a specific period of time. Cueto's absence is currently indefinite.
"I don't know the exact date of which he will return," Price said.
Mark Sheldon is a reporter for MLB.com. Read his blog, Mark My Word, and follow him on Twitter @m_sheldon. This story was not subject to the approval of Major League Baseball or its clubs.