The two-time A-League champion club has come out firing amid reports that FFA have hatched a plan to install a third team in Sydney if or when Wellington Phoenix are kicked out of the competition.
Phoenix's application for a 10-year extension to their A-League licence that expires at the end of the current season was rejected by the governing body on Monday.
While Wellington have been offered a four-year extension, the club is unlikely to take up the offer, which would leave the competition with nine teams.
Such an eventuality would speed up the process of installing a new team, most probably coming from southern Sydney.
"A-League clubs must be able to operate with the confidence that their market place won't be cut in half at the drop of a hat," Barlow said.
"If FFA can't provide clubs with this assurance then what is the point in investing further and what is the value of an A-League licence?"
Barlow claimed that a new team in the city's south would impinge on the Sky Blues' membership, which stands at a record of 11,657.
"South Sydney is a critically important region for Sydney FC," he said.
"Twenty-five per cent of our members live south of Mascot, 40 per cent of our junior members live south of Mascot and we have more members from Sutherland than from any other region of Sydney.
"A new team in Sydney - in the heart of arguably our most important region - would effectively cut our market in half.
"It would be a devastating blow for our club and certainly not what we signed up for or agreed to invest in 11 years ago."
Barlow said he disapproved of the way FFA have dealt with Phoenix's off-field problems that include poor crowds and viewership.
"I don't agree with the way Wellington Phoenix are being treated throughout all of this," Barlow said.
"They are a professionally run and financially stable club and they deserve to be treated with more respect than they are currently."
The club's supporter group, the Cove, have thrown their support behind Phoenix.
"For nine seasons Wellington Phoenix and Yellow Fever have been a vibrant and important part of our league," a Cove statement read.
"The Cove put our support fully behind the #savethenix campaign.
"Sutherland Shire is a key source of Sydney FC support, almost a third of our number come from there, placing a team in that area in an ill-conceived attempt to replicate the WSW-SFC rivalry is doomed from the start.
"There is no pent-up demand, as there was in Western Sydney, and nine derbies instead of three will simply take the special away and make it commonplace. We urge the FFA to rethink their plan before doing permanent damage to our sport."
Western Sydney Wanderers preferred not to comment on this week's developments.
