Officials have said in the past that drug gangs may be using rehabilitation clinics to recruit drug dealers, or may be targeting them to eliminate rivals.
Pilar Macias, who lost her brother Juan Carlos in the attack, said: "He was recovering [from cocaine addiction] - he wanted to get back on the right track and they didn't let him, they didn't give him a chance.
"This is going to kill my mother … She is very sick and this is going to kill her."
The attack at the Anexo de Vida centre comes two weeks after attackers shot dead 18 patients at another clinic in Ciudad Juarez.
Five men were killed in an attack on another rehabilitation centre in June.
The authorities have not said if any of the attacks are linked to each other.
Ciudad Juarez has seen the highest levels of drug-related violence in Mexico, with more than 1,300 deaths so far this year.
The Mexican authorities have sent hundreds of extra troops to the north of the country since March in attempt to quell the violence but little progress appears to have been made.
Gang and drug related violence has claimed at least 13,500 lives since Felipe Calderon became president in 2006.