Three men opened fire at a cafe used by Real fans in the town of Balad on Friday.
The club said 16 fans died and more than 20 were injured in the attack.
In a statement, the club said:
"The club expresses its great sadness and offers its regards and condolences to the families and friends of the victims. Real Madrid extends all of its solidarity to the people of Iraq, who suffer the excessive injustices of extreme violence.
"The Real Madrid players will tomorrow (Saturday) wear symbolic black armbands as a sign of their mourning and respect. Football and sport shall always be spaces in which to come together and in which harmony and peace reign and with which no form of barbaric terrorism will be able to compete.
Today Madridismo across the whole world cries for its supporters, who shall never be forgotten.
Real Madrid face Deportivo La Coruna in the final game of the Liga season on Saturday - Real must better Barcelona's result against Granada to become champions.
Liga president Javier Tebas Medrano wrote on Twitter: "Terrorism has attacked football. We are with the victims and their families. We were going to travel (to Iraq) this month, but it was put off for security reasons. We will be back to support the people of Iraq."