Tebas said the inquiry had been requested by Eldense's board of directors following the defeat which relegated the Alicante-based club to the fourth tier.
After the game, in which Barcelona B led 8-0 at halftime, Eldense striker Cheikh Saad also made match-fixing allegations on RAC1 radio.
"We are going to look into it because the Eldense board have asked us to and the result at half time (8-0) was out of the ordinary," Tebas told reporters at an event.
"We're going to investigate because there are certain collateral issues with an Italian investment group that bear the hallmarks of the possible involvement of an international betting ring which may be related to match-fixing."
Eldense chairman David Aguilar said he had suspected possible match-fixing at the club "for a few weeks" and added that police were also looking into Saturday's game.
Reuters were unable to confirm this on Monday.
Aguilar denied weekend reports that the club had suspended all sporting activity and were not intending to fulfil their fixtures. He said the team will play next weekend against Sabadell.
There is no indication that Barcelona B players had any involvement with the alleged match-fixing.
"It's an internal topic for that club and Barcelona have nothing to do with it," Barcelona president Josep Maria Bartomeu said on Monday.
(Reporting by Rik Sharma, Editing by Neil Robinson)
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