The airline has also said it will work to assist passengers “as efficiently as possible” if there are further cancellations in the coming days.
It comes after three return flights were cancelled yesterday due to the virus while Covid and strikes were blamed on 13 cancellations over the weekend.
The flights departing from Dublin Airport affected today were EI3250 to Edinburgh at 6.40am, EI650 to Frankfurt at 7am and EI552 to Lyon at 11.40am.
Further cancellations were confirmed for EI684 to Geneva at 1.15pm, EI356 to Munich at 4.25pm, and EI 610 to Amsterdam due to depart at 6.15pm.
As a result, the corresponding return flights from those destinations due to arrive in Dublin Airport today have also been cancelled.
In a statement to Independent.ie the airline said that it is working to arrange alternative travel options for those impacted.
“Due to a spike in Covid cases Aer Lingus has been forced to cancel 6 return flights from Dublin today, Wednesday 29th June. Our teams are working to secure alternative travel options for customers in each case and wish to apologise to those impacted for the inconvenience.
“Just over 1pc of Aer Lingus flights have been impacted by cancellations this month.”
The airline also said that it will seek to re-accommodate travellers in the event of further cancellations in the coming days.
“Should crew illness require the cancellation of additional flights in the coming days, we will seek to re-accommodate passengers on the next available services as efficiently as possible.
“Aer Lingus anticipated the return of demand for travel once Covid restrictions were removed and built appropriate buffers into our plans in order to deal with a reasonable level of additional disruption.
“System pressures and ongoing issues at some airports and among third party suppliers have created considerable operational challenges which have been compounded by a significant spike in Covid cases in recent days,” the statement said.
It added: “We have shared detail regarding customers’ rights the airlines’ obligations under Regulation (EC) 261/2004 which can be found here: www.aerlingus.com/support/legal/regulation”.
While Dublin has been the main airport affected, a return flight from Shannon Airport to Boston was also cancelled today.
On Sunday, a total of 13 flights to and from Dublin Airport were cancelled with this mainly due to air traffic control strikes in France, Italy and Spain.
Issues at other airports and among third party suppliers were also cited as reasons for flight cancellations over the weekend with Aer Lingus apologising for the flight turmoil.
Ryanair have said that there have been some “minor delays” to its schedule as a result of air traffic control staff shortages, which the company said were “entirely beyond” its control.