It comes after a spate of positive drugs tests among the country's athletes and fresh allegations of corruption.
Kenya has not been able to provide the assurances Wada is seeking and will be placed on a 'watch-list' of nations at risk of breaching the agency's code.
The East African country, whose athletes are dominant in distance running, will be given two months to bring in new legislation and funding, or automatically be declared non-compliant with Wada.
That could mean a possible ban from the Olympics, which take place later this year in Brazil, and other major events.
A Wada statement said while "some progress has been made" with the Anti-Doping Agency of Kenya (Adak), there is "still a lot of work required".
It said that, following a series of questions to Kenyan authorities, it had not received the assurances it needed and was still awaiting "concrete plans" on government funding for Adak, legislation and anti-doping rules.
"This is now a matter for our independent compliance process," Wada said.
As of January 2016, 18 Kenyan athletes were suspended for doping The best known athlete suspended is Boston and Chicago Marathon winner Rita Jeptoo
The 18 athletes are serving bans totalling 55 years Lilian Moraa Mariita was given the longest ban of any Kenyan athlete - eight years for taking steroids
Russian athletics is already banned from international competition after allegations of state-sponsored doping - and must prove it is Wada-compliant before sanctions are lifted.
"The biggest threat is the declaration of non-compliance and the possible consequences of that," said Christine Wambui Mugera, head of the regional anti-doping organisation in East Africa.
"The International Olympic Committee and other major event organisers, international federations, have the capacity to refuse entry for athletes from a country that has been declared non-compliant.
"But we have to wait to see how this plays out."
The Kenyan government told the BBC it was taking the threat of doping "very seriously" and a newly established national anti-doping organisation (Nado) would soon be operational.
For several months, Wada has been trying to persuade Kenya to set up an effective national agency so more drug tests can be conducted but progress has been slow.
Legislation has yet to be passed by the Kenyan parliament and proposed annual funding of 500m Kenyan shillings (£3.5m) is still to be released for Adak.
It now appears Wada has run out of patience.
A taskforce met with Kenyan officials in Nairobi last week and asked for certain assurances by Thursday.
But Kenya has now been referred to Wada's compliance review committee.
"A fully functional Nado is… a vital step for a country of Kenya's sporting stature to take if it is to effectively protect clean athletes," said David Howman, Wada's director general.
He said it must be established "at the earliest opportunity".
BBC