The Prospect union said the walkout on July 29 will mark an escalation in the industrial action which has been going on since January.
HIAL is planning to centralise operations in Inverness and introduce remote integrated air traffic control services for five airports: Inverness, Dundee, Stornoway, Kirkwall and Sumburgh.
Prospect said members will take action because the plans will remove high value jobs from remote communities, which will have a strong impact on those economies and result in redundancies as people are unwilling to relocate to Inverness from the communities they love and serve.
HIAL said the strike action will “inflict additional disruption and inconvenience on passengers”, though it will work to keep this to a minimum.
David Avery, Prospect negotiator, said: “Our members have been forced into this escalation of industrial action to protect the communities they serve.
“HIAL’s plan will remove high value skilled jobs from economies that can ill-afford to lose them, having a substantial negative impact on those communities.
“The Scottish Government has the power to step in on this debate but the minister (Scotland’s Transport Minister Graeme Dey) hasn’t even taken the time to meet the local councils involved, or indeed his own MSPs to discuss the impact of the remote towers project.
“We have since had the bizarre situation where UK minister Michael Gove discussed the matter with Comhairle nan Eilean Siar while the minister refuses.
“Prospect members are not averse to change but it has to be done in a way that maintains jobs and skills in remote communities. HIAL needs to halt these plans now so our members can get on with their jobs.”
The industrial action so far has included staff working to rosters, a ban on overtime, refusing shift extensions (except for search and rescue, emergency and medical flights) and refusing to train new controllers.
Inglis Lyon, HIAL’s managing director, said: “We are extremely disappointed to have received this formal notice without any prior intimation from Prospect.
“This action will inflict additional disruption and inconvenience on passengers at such a crucial time for the communities of the Highlands and Islands.
“It will also have an impact on the aviation sector which serves them and which is seeking to get back on its feet following the worst of the pandemic.
“We will work closely with our airline partners to keep disruption to a minimum and apologise for the undoubted inconvenience this action will cause.
“Given the positive response from Prospect to the policies relating to the modernisation project, this is bitterly disappointing.
“We ask that Prospect work with HIAL on completing the policy work before considering strike action and to meet with HIAL in the interim to agree how this might happen.”
The Scottish Government has been asked for comment.