The impact on its Northern Ireland operations is not clear.
The company said it "will be evaluating the impact on our Belfast operations" and it could not "elaborate further at this point in time."
It is already in the process of axing 1,080 posts in Northern Ireland, about 20% of its workforce in the region.
The Montreal-headquartered company said on Friday it will cut about 7,500 jobs globally, with about two-thirds of those in its railway division.
The rest of the cuts will be made in the aerospace part of its business - with consequences in Belfast.
The trade union, Unite, said it was "deeply concerned."
Spokesman Davy Thompson said: "We will work over the coming period to minimise any potential job-losses and if necessary we will strive to deliver the best possible outcome for those affected.
"We can only hope the announcement will mean the company is better positioned to achieve long-term growth and safeguard future employment."
Mr Hamilton said the announcement "will come as a great shock to the Northern Ireland workforce".
He added: "We will do absolutely everything we can and take every opportunity to highlight to senior decision makers in the company the strength of Bombardier's Northern Ireland operations and the skills of the workforce.
"I will do everything I can to fight to save as many Bombardier jobs in Northern Ireland as possible."
However, Bombardier's chief executive officer Alain Bellemare said the firm will will also add jobs in some areas of its manufacturing business, including the C Series and Global 7000 business jet.
Both of those jets provide employment in Belfast.
"There will be a significant offset in our resizing," he told the Bloomberg news agency.
Asked for more details, Mr Bellemare said the company would probably look to hire more than 3,750 employees for "major" programs, but was not specific about locations.
NI Economy Minister Simon Hamilton has vowed to "fight to save" Bombardier jobs in Belfast, with the firm planning to cut 7,500 posts worldwide.