Thomas J Henry Law said on Sunday that it had filed "one of the first cases in Travis Scott Astroworld festival catastrophe".
Kristian Paredes, 23, is the plaintiff, and he was one of the "severely hurt" at the event on November 5.
A second lawsuit was filed in Houston state court on behalf of a guy who was injured in the crush. Manuel Souza's lawyers sued Scott, the concert promoter Live Nation, and others, alleging that they were liable.
Scott said he was "truly saddened" by what happened in a tweet on Saturday. He promised to work "in collaboration with the Houston community to heal and support the families that are in need."
At NRG Park in Houston, some 50,000 people were in the audience when the crowd began pushing towards the stage as Scott was performing, resulting in chaotic scenes. 25 individuals were brought to the hospital as a result of the incident, and more than 300 others were treated on the spot for minor injuries.
According to the complaint, as Scott took the stage, Paredes, a Texas resident who is also suing Live Nation and the venue, "felt an immediate push" at the front of the general admission area.
"The throng became tumultuous, and a stampede ensued. Many people pleaded with security officers hired by Live Nation Entertainment for assistance, but they were turned down."
Scott "had incited mayhem and turmoil at earlier gatherings," according to the lawsuit, which says "defendants knew or should have known of [Scott's] prior conduct."
It accuses Drake, a Canadian rapper who performed alongside Scott during his headlining set, of contributing to the crowd's rush to the stage.
"Drake helped excite the crowd as he came onstage alongside Travis Scott, despite knowing of Travis Scott's prior actions," the complaint claims.
Even as the "crowd became out of control" and the "crowd mayhem continued," he continued to perform, according to the report.
The lawsuit comes as more information about individuals who died becomes available. According to Harris County authorities, the names of the dead were released on Monday, with victims ranging in age from 14 to 27 and hailing from Texas, Illinois, and Washington.
Franco Patino, a 21-year-old mechanical engineering technology student, was among the victims. In an interview with the Associated Press, Franco's father, Julio Patino, described him as a charismatic, energetic leader who was engaged in his community and dedicated to assisting individuals with disabilities.