It was put up at Stronsay Junior High in Orkney as part of a BBC trial testing live radio broadcasts over 5G mobile networks.
The trial, which began earlier this year, was initially due to run for six weeks but was later extended until the end of September.
Some parents are concerned about potential health risks relating to the project.
One family withdrew their three children last term while another family did not send their children to school on Tuesday, the first day of the new term.
Their father, Duncan Bliss-Davis, whose six children are aged between five and 11, said they were concerned about potential risks.
He said: "The NHS are saying children should only use mobile phones for essential purposes and keep calls short and Public Health England say excessive use of mobile phones by children should be discouraged, yet there is a mast on the school and 20 handsets have been given out.
"One of the reasons we moved here was to get away from the explosion of mobile phone masts and mobile phones.
"People keep talking about how we've been using phones for years with no ill effects but my point is that is not for a person's lifetime."
The children are currently being home schooled but Mr Bliss-Davis said they will probably go back to the school, which has around 30 pupils, if the trial ends in September.
He added: "To us educating our kids is very important and when the trial was just going to be six weeks we thought we could take them out or leave them there and it was only for a short period of time so we left them in but then they extended it."
The 20 handsets were given to local adults as part of the trial.
In a letter to parents, the BBC said: "The equipment we're using for the 5G broadcast radio trial is based around 4G technology, which is widely used across the UK, and the radio frequencies being used are the same that are used to broadcast TV.
"The trial is fully compliant with advice from Public Health England that any exposure to radio waves must comply with guidelines set out by the ICNIRP, an independent international commission recognised by World Health Organisation.
"Those guidelines recommend that exposure to radio waves should be below a certain power level - and the power levels we measured are 1,000 times lower than that level."
Orkney Islands Council said it worked with the BBC to identify Stronsay, which has poor connectivity, as a suitable location for the trial.
A council spokesman said: "The council obtained guidance on 5G safety from Public Health England (PHE) before agreeing for the 5G equipment to be installed in Stronsay.
"PHE is the national body that takes the lead on public health matters involving radio frequency electromagnetic fields, or radio waves, used in telecommunications.
"PHE's advice is that there should be no consequences for public health."
He added: "The BBC has also said that there is no reason to believe there are safety concerns surrounding the trial as the equipment being used is based around widespread 4G technology and is operated at very low frequencies.
"The power levels the BBC has measured in and around the school are 1,000 times below the recommended levels for these frequencies."
The council has agreed the 5G antenna can remain in operation until September 30.