The rights group said it interviewed witnesses, collected photos and reviewed video footage indicating that chlorine bombs were dropped from government helicopters during the offensive from November 17 to December 13.
Around 200 people were injured by the toxic gases used on opposition-controlled areas of the northern city, according to HRW.
The actual number of chemical attacks could be higher, said the group, adding that journalists, medical personnel and other credible sources had reported at least 12 attacks in that period.
The report detailed attacks on a playground, clinics, residential streets, and houses that left scores of people struggling to breathe, vomiting and unconscious.
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"The chemicals would affect the children most severely... they inhale these smells and they end up suffocating," said a first responder quoted in the report.
Syrian forces, backed by Russia, launched an offensive in November to seize east Aleppo, a key battleground in Syria's nearly six-year war, and the regime announced on December 22 that it had taken full control of the city.
Chlorine use as a weapon is banned under the Chemical Weapons Convention, which Syria joined in 2013 under pressure from Russia.
Human Rights Watch urged the Security Council to impose sanctions on senior leaders in the chain of command, but such a move would likely to be vetoed by Russia, Syria's ally in the war.
The group said there was no evidence that Russia was directly involved in the chemical attacks, although Russian aircraft did play a role in the military offensive against opposition fighters in east Aleppo.
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