Only three other African nations have previously made it to the quarter-finals.
Morocco became the first African country in history to reach the World Cup semi-finals by beating Portugal 1-0 on Saturday.
Youssef En-Nesyri scored the winning goal in the 42nd minute to continue Morocco’s improbable run that has generated an outpouring of pride in the Arab world during the first World Cup to be staged in the Middle East.
"The Moroccan team is making the hearts of all Moroccans beat as one," said Euronews Correspondent Kawtar Wakil.
"This is something we've not seen since 1986 and the team's performance has been a shining light not only for Moroccans around the world but all Arab and African football fans."
37-year-old Cristiano Ronaldo, one of football’s greatest players, didn't start for the second straight game but came on as a substitute in the 51st minute.
Morocco will play either France or England in the semi-finals, joining Croatia and Argentina who qualified for the final four on Friday.
It is a seminal moment in World Cup history, with an African nation finally advancing to the levels typically only reached by European or South American teams.
Cameroon (1990), Senegal (2002) and Ghana (2010) all reached the quarter-finals but got no further.
Mohammed Dailal, a Morrocan fan in Tangier, praised the support his country's team had received, especially from fans in the Arab world.
"We are so proud to be Moroccan and we are happy because the whole Arab world is behind the Moroccan team," he told Euronews. "The unity has been really heartwarming to see".
Another Morocco supporter Aymen Laouad said: "We will move forward and fulfil the dreams of all Moroccans".
They will play next on 14 December, against either France or England who are playing Saturday night.
The result means there will likely be no World Cup title for Cristiano Ronaldo in what is set to be his last appearance at football's biggest tournament.
Ronaldo walked off the field in tears.
Born in the Moroccan city of Fez, En-Nesyri's goal was described as a historic moment.
His phenomenal relaxation trapped goalkeeper Diogo Costa, who came out at the wrong time.
Following a perfect cross from Yahya Attiat-Allah, En-Nesyri, who plays for the Spanish side Seville, powerfully lowered his head, the ball hit the ground to bounce and then he slammed it into the back of the net.
An African team got close to the final knockout stages of the World Cup in 1990 when Cameroon failed to get into the quarter-finals, being beaten by England.
In 2002, Senegal was stopped at the golden goal by Turkey, losing 1 -0.
Before En-Nesyri, the Ghanaian Asamoah Gyan got the closest to the last four, but he smashed his last-minute penalty (120th + 2) on the Uruguayan crossbar, after the famous handball of Luis Suarez in 2010.
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