The city was among five in the UK bidding to host the title, with the winner expected to be announced next week.
However it emerged that the European Commission has told the UK Government a British city cannot hold the title in 2023 due to Brexit.
Writing to Westminster Culture Secretary Karen Bradley, Ms Hyslop said: “Dundee have put a considerable amount of time, effort and expense into scoping out their bid and are excited about the many benefits such a bid would generate in Dundee, Scotland, the rest of the UK and Europe.
“A successful bid will deliver 1,600 new jobs, an additional 500,000 visits to the city during the year and the programme of events would leave a lasting legacy. Dundee’s bid has the full backing of the Scottish Government and cross-party support in the Parliament.
“So I am extremely disappointed to learn that the significant contributions the Dundee team and Dundonians have put into developing their bid may be wasted as a result of the UK Government’s position to pursue a damaging Brexit.”
Ms Hyslop called on Ms Bradley to meet Dundee’s bid team and provide an “indication as to what steps the UK Government intends to take with the EU to address this unacceptable position”.
She has also written to Martine Reicherts, director general for education, youth sport and culture at the European Commission, urging her to reconsider the decision not to allow Dundee to participate.
She said: “Whilst the preference of the Scottish Government would be to remain a full member of the European Union, we sincerely hope that cultural collaboration is an area which will form part of the UK’s future partnership with the EU.
“We will do our utmost to persuade the UK Government of the importance of continuing to participate in European partnerships like the European Capital of Culture and in that vein I would urge you to reconsider this decision.”