Uefa imposed the penalties after objects were thrown at Celtic players in the Champions League qualifier.
Linfield's South Stand lower section 1 will be closed for one European game.
Celtic's Leigh Griffiths has received a one-match ban for provoking spectators while his club have been fined £4,000.
Griffiths tied a Celtic scarf to a goalpost after the final whistle in Friday's game.
Earlier on Thursday, Uefa also charged Celtic over an "illicit banner" displayed during Wednesday's second-leg game in the Champions League tie.
The Glasgow club have also been cited for a "kit infringement" and "blocked stairways" at Celtic Park following Wednesday's 4-0 victory.
A Uefa spokesperson said that the illicit banner charge related to the banner "portraying a person in a paramilitary uniform".
That case will be dealt with by the Uefa control, ethics and disciplinary body on 28 July.
Linfield have been handed a partial stadium closure for their next European tie and fined £8,850 following incidents in last week's game against Celtic at Windsor Park.