Sports Minister Kelvin Cruz announced the ban after incidents before the match on Thursday night at the entrances to the Felix Sanchez Olympic Stadium in Santo Domingo.
Video posted on social media showed groups of fans forcing some entrances, with one gate damaged.
"What we saw yesterday with a gate at the Felix Sanchez, a sports facility that has cost millions and millions of pesos to make it shine, is unacceptable," Cruz said, citing a zero-tolerance policy on indiscipline.
Dominican Republic President Luis Abinader backed the decision.
The Haitian Football Federation did not immediately respond to a request for comment on the ban.
In a post on X after the match, the federation called it a "beautiful night for Haiti, beautiful night for the island we share," adding: "On the field, competition; off the field, respect for the neighbour."
Haiti won the match 4-1, with Sunderland striker Wilson Isidor scoring twice. The win gave Haiti nine points in Group A, while the Dominican Republic stayed on six. Haiti play Costa Rica in San Jose on Sunday.
Isidor was filmed saying, "Hispaniola is Haiti." Hispaniola is the Caribbean island shared by the Dominican Republic and Haiti, which have long clashed over migration and border security.
Dominican federation president Jose Deschamps called Isidor's remark "a lack of respect for national sovereignty" and said the federation would file a complaint with FIFA and Concacaf.
The two sports governing bodies did not immediately respond to requests for comment.
Haiti's embassy in Santo Domingo said the remarks, made "in the heat of competition and the intensity characteristic of sporting events", did not reflect the position of the Haitian government and thanked Dominican authorities for the event.
"Sporting rivalries must not call into question relations of good neighborliness and mutual respect that must prevail between the two states," the embassy said in a statement.
Haiti and the Dominican Republic have long had tense diplomatic relations. Abinader's government has stepped up deportations of undocumented Haitians since 2024, when it pledged to deport up to 10,000 people a week.
Sport has been drawn into the neighbours' disputes before.
In 2023, after Abinader shut the border in a dispute over a Haitian canal on the shared Massacre River, Haiti's sports ministry ordered its football federation to stop staging national team matches in the Dominican Republic.