Stuart Patrick, chief executive of Glasgow Chamber of Commerce, has asked to meet Nicola Sturgeon to highlight concerns over the impact the purchase could have on the commercial interests of Scotland's second busiest airport.
It comes after Scottish Government confirmed on Saturday that the sale of the Ayrshire hub from New Zealand owners, Infratil, had been completed in a £1 deal, seven weeks after the decision to take the loss-making airport into public hands was first announced.
In a letter to the Deputy First Minister, Mr Patrick said: "We are conscious of the established impact that a successful international airport has on the economic development of a city and the damage that can be done to investment potential if the city airport is unsuccessful.
"In response to feedback from our members, Glasgow Chamber is paying particular attention to the growth of Glasgow International Airport's offer of direct routes to markets of relevance to business, connections to Heathrow as our primary international hub airport and the expansion of connections to other important hub airports such as Dubai."
In particular, members of the Glasgow Chamber are seeking clarification on how the takeover will affect Government marketing support for air routes out of Glasgow and future plans to improve surface access to attract new airlines and additional services.
They also raise concerns about the impact Prestwick's ownership will have on Glasgow airports' ability "to share commercially confidential information about its strategic intentions with Scottish Government officials".
A spokesman for Glasgow Airport said bosses had been assured by the Scottish Government that its plans for Prestwick "will be entirely commercial and will not harm any other airport", but were now seeking a further meeting "to stress the importance of maintaining a fair and competitive landscape" in light of the weekend's announcement.
Gordon Matheson, leader of Glasgow City Council, said the Government's actions in relation to Scottish airports appeared "unplanned and ad hoc", and demanded a clear plan on how it would support "continued growth of Glasgow Airport as a successful and thriving passenger airport".
A spokesman for Transport Scotland said: "Investment by the Scottish Government will be undertaken on a commercial basis. We expect investment to generate a long term return for taxpayers' money. This investment will help ensure the continuation of robust competition between airports in Scotland."