Cruise business director Parsons joined the Glasgow-headquartered agency chain in 2006.
A Barrhead spokesperson said: “We would like to thank Catriona for all her hard work and her contribution over the years. We wish her all the best in the future.”
They added: “We will be announcing an internal restructure shortly.”
Barrhead was acquired by US travel group Travel Leaders last year. And in January, Jacqueline Dobson was promoted to president replacing Sharon Munro.
Earlier this year, Dobson revealed a third of Barrhead’s holiday sales were for cruise, a trend she said the business expected to “continue to accelerate” throughout 2019.