The Spaniard turned professional with the Italian ProTeam this year but his debut campaign was cut short when he began to suffer a series of severe headaches in August.
Medical tests soon revealed a brain tumour, which increased in size in the subsequent weeks, leading to an urgent need to operate.
Grávalos went under the knife in hospital in Zaragoza on Thursday in a procedure that was "complex and lasted several hours", according to the Eolo-Kometa team.
The operation was said to be a success, with the doctors satisfied with the outcome.
"At the express wish of the rider and his entourage, the situation has been kept discreet, while awaiting the surgical intervention and the subsequent start of the rehabilitation process, two moments for which the doctors had advised him to be as stress-free and calm as possible," read an update from Eolo-Kometa on Saturday.
The statement also included a message from Grávalos' family: "We would like to publicly thank all the professionals at Lozano Blesa for their attention and care, and especially the great work done by the whole team led by Dr. del Río."
Grávalos rode as a stagiaire last summer for Eolo-Kometa, the team set up by Ivan Basso and Alberto Contador, before joining on a full-time professional contract this year.
He has had limited outings so far, finishing outside the time limit at Strade Bianche and GP Indurain in the spring before putting together a string of one-day races in June and July. He finished 84th at the week-long Settimana Ciclista Italiana in July before riding three one-day races in Spain, the last of which saw him finish 48th at the Circuito. de Getxo on August 1.
It is unclear at this stage how Grávalos' condition and treatment will shape his future career, although it is hoped the swift removal of the tumour will allow for a full recovery. Earlier this summer, Belgian cyclo-cross rider Jolien Verschueren died after a brain tumour turned malignant.
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