The 27-year-old had been due to face Wladimir Klitschko in a rematch, before the Ukrainian retired on Thursday.
The WBA says Joshua and Ortiz have 30 days from 3 August to agree the fight.
Joshua, who beat Klitschko at Wembley in April, has also been told he must face IBF mandatory challenger Kubrat Pulev before 2 December or risk being stripped of his belt.
There had been plans for Joshua to fight Klitschko in Las Vegas on 11 November and Ortiz's manager, Jay Jimenez, has said his fighter could fill the void.
Jimenez told Boxingscene: "We are next. We have no problem fighting on that date of November 11th in Las Vegas.  Our mandatory takes precedent over Pulev's and they know that."
Ortiz, 38, has 23 knockouts from 27 wins, while Pulev, 36, has one defeat in his 26 fights, with 13 stoppages.
Joshua holds two of the four major belts, with New Zealand's Joseph Parker the WBO champion, while American Deontay Wilder has the WBC belt.

National Guard troops are now pulling out of the city. The curfew was put in place on Tuesday, after protests over Freddie Gray's death turned violent.
Six police officers are facing criminal charges over the death, which has been ruled a homicide. They deny wrongdoing.
Gray was arrested on 12 April, and died a week later from injuries sustained in the back of a police van.
Under the curfew, residents were ordered to stay home from 22:00 until 05:00, and officials had been expected to keep it in place for another day.
But on Sunday morning, Baltimore Mayor Stephanie Rawlings-Blake said she did not want to maintain it any longer than was necessary.
"My goal has always been to not have the curfew in place a single day longer than was necessary," the mayor wrote on her Twitter account. "I believe we have reached that point today."
Protests in Baltimore have continued since looting and arson erupted on Monday night - which  prompted the deployment of the National Guard. However the demonstrations have been largely peaceful since then.
Maryland Governor Larry Hogan said the state of emergency in the city would not be lifted until the last soldier had left.
Correspondents say the charges against the officers - ranging from manslaughter to second-degree murder - have eased tensions.
The charges were announced on Friday by the city's top prosecutor Marilyn Mosby. But a lawyer for the six officers insisted they had done "nothing wrong".
Police have admitted that Gray, 25, was not secured in the van by a seatbelt and that his requests for medical attention while being transported were denied.
Gray's death is the latest in a series of killings of black men at the hands of police in the US which have sparked rioting and national debate.
What we know about Gray's death
Is Baltimore starting to heal?

Police said the child, who is thought to have been shot by her father who was found dead at the scene in Northiam, is seven years old.
Ch Supt Neil Honnor said a firearm had been recovered, but would not confirm the relationship between the girl and the man.
The body of the man was found in a car parked outside a house in the Spring Hill area of the village.
Prayers have been said at the injured girl's school, Beckley Church of England Primary in Beckley near Rye.
The area around the scene has been cordoned off since the shooting, which happened at about 16:00 BST on Thursday.
Ch Supt Honnor said officers had identified "the perpetrator of the offence".
"This does not appear to be an incident that's necessarily related to Northiam other than the fact that it happened there.
"We believe this is a domestic-related incident," he said.
In a statement, a spokeswoman for the Beckley CE Primary said: "We have received confirmation that the child who was shot is a pupil at our school.
"This is a dreadfully sad and shocking incident and the whole school community are praying for her and her family."
The girl is being treated at King's College Hospital in London.
British heavyweight Anthony Joshua has been ordered by the WBA to defend his title against Cuba's Luis Ortiz.
[NEXT_CONCEPT]
Baltimore has lifted an overnight curfew imposed after riots sparked by the death of a black man in custody.
[NEXT_CONCEPT]
A young girl shot in the head in East Sussex remains gravely ill in hospital.