Jones died of a heart attack last week. He was 66.
"My understanding is they want to avoid a media circus and ... the family wants to keep it very, very low-key and very, very private," Dolenz told Billboard.com. "And you can imagine as soon as one or two or any of us were to show up, it would very quickly be degraded into something that I don't think his immediate family would want to deal with. So I'm kind of respecting their wishes, whatever their wishes may be."
In addition to the private funeral Jones' family is planning in Florida, public memorials are being scheduled in New York and Jones' native United Kingdom. No dates for any of the ceremonies have been announced yet.
"He obviously had fans and family and associates on both [U.S.] coasts and two continents," Dolenz told Billboard.com. "It's pretty early days, you know, to be making too many plans. I'm still in shock."
Jones, Dolenz and Tork toured together last year to mark The Monkees' 45th anniversary. The foursome last played together in 1997.