"Many of us have daughters who have had pre-prom tans," said Hollinger, D-Baltimore.
Tanning bed operators argued at a hearing last month that tanning beds actually prevent sunburn by allowing people to build up "base tan."
Ruth Smith, owner of What a Tan in Hagerstown, testified against the bill.
Marcia Swain, a Hagerstown health educator, testified in favor of the legislation. She said three members of her family, all Washington County farmers, have died from skin cancer in the last 10 years.
Ultraviolet rays emitted by tanning beds are suspected to have links to malignant melanoma and immune system damage, according to the Federal Trade Commission's Web site.
In addition to requiring a doctor's permission for young people, Munson's bill would have regulated tanning beds in the state for the first time.
Under Munson's proposal, violators of the law would have faced a fine of up to $100 for the first violation, $250 for the second violation and $500 for the third violation.
Munson blamed the defeat of the bill on industry lobbyists. He said he plans to revisit the issue next year.
Hollinger said the committee has asked state health officials to review safety studies of tanning beds.