The two blasts killed at least two people and injured at least 84, Afghan officials said as cited by the newspaper.
Following explosions, fighting erupted near the consulate, he German Foreign Ministry reported.
"There has been fighting outside+on the premises of the German Consulate General. Afghan security+@ResoluteSupport forces are on-site," the ministry said.
Later the ministry said on Twitter that the fight was over.
"#Mazar: The attack on the GER Consulate General is over. We are grateful to the brave Afghan+@ResoluteSupport forces for their intervention," the ministry wrote.
The Taliban has claimed responsibility for the attack.
Afghanistan is currently in a state of political and social turmoil, with government forces fighting the continuing Taliban insurgency. The instability has persisted in the country since the 2001 US-led invasion aimed at defeating the Taliban and al-Qaeda in the wake of the 9/11 attacks in the United States.