The state’s Public Regulation Commission unanimously agreed to have the utility Public Service of New Mexico (PNM) bill Facebook for half the cost of the line.
Some officials said the decision could have a potential "chilling effect" on economic development and renewable energy investment.
Facebook agreed to buy power from Avangrid’s 166MW La Joya project near Encino, New Mexico. It is due online in 2020.
PNM had been seeking permission from regulators to pass on $39m of the cost of the transmission line to consumers.
The commissioners however said the line would only benefit Facebook and wholesale electricity buyers – rather than ordinary ratepayers.
Two state cabinet secretaries have since written to the PRC to express their concern about the decision.
"If New Mexico does not keep all of the promises made to this company, we may not have the opportunity to land another project of this calibre for years," wrote economic development secretary Alicia Keyes and energy, minerals and natural resources secretary Sarah Cottrell Propst.
The utility can ask for a rehearing, or appeal against the decision at the state Supreme Court.
Facebook opened the $1 billion data centre in Los Lunas in February.
Developing and financing wind-friendly transmission in the US is contentious when commercial and industrial customers buy the renewable energy.