Opponents said the plan would be unworkably complicated, would pressure states without sales taxes to adopt them and would encourage companies to move overseas, where they said sales taxes could not be enforced.
"It tramples on states' rights," said Sen. Kelly Ayotte, R-N.H.
Online businesses with less than $1 million in annual sales would be exempted from having to collect the levies.
In states with sales taxes, online buyers are currently supposed to pay a tax on their purchases but the requirement is seldom enforced.
Twenty-six Republicans voted to endorse collecting Internet sales taxes and 19 Republicans voted against it. Democrats backed the proposal, 49-5.
Friday's vote was on an amendment to the 2014 budget the Senate was debating.