The company is closing its call centre at Springvale Business Park off the Springfield Road,
It provides outbound calls to potential customers for insurance firms RIAS and Castle Cover.
The firm said the Belfast site has become “increasingly uneconomical” due to changing consumer behaviour.
A 90-day redundancy consultation period has started.
SDLP MLA Alex Attwood said it was a devastating blow for west Belfast and had not been expected.
“I am urging Ageas Belfast to hold back on any final decision, to meet political representatives, the enterprise minister and Invest NI to seek answers to this critical situation,” he said.
“Those workers had no idea of anything that was coming and, as best as I can determine, nobody in any of the government or economic agencies in Northern Ireland knew that anything was coming,” he said.
“All the indications were over the last number of years that business was good.”
The firm has said it will “do all it can to help employees find alternative employment”.
One employee said the workers had had no advance notice of the move and it had come as a “terrible shock”.
Sinn Féin MP Paul Maskey said he was shocked by the news.
“I was extremely disappointed that Ageas Retail have announced a 90-day consultation on the future of 200 jobs at its west Belfast site.
“This decision has come out of the blue to staff who are understandably shocked. Some of them left today in tears concerned about their future.”
Mr Maskey said he would be “engaging” with the company throughout the consultation process to ensure that everything possible was done to help staff find alternative employment.