The midfielder, who is set to be offered an improved contract next month, turned 20 last week and despite his age and relative inexperience he has become a key player in the side.
Almost half his 33 club appearances have come under Martinez and he has started 12 of their 15 Barclays Premier League matches this season.
Martinez is mindful of the workload on younger players but is more than confident Barkley's special talent can cope with the rigours of a long campaign which will only get more difficult in the new year.
"Physically he is one of those players who is really capable," said the Spaniard.
"He is not like other footballers. Normally you get the technical player and the physical player and in Ross's case it is both, which is quite unique.
"It is important to measure him weekly to make sure he doesn't burn himself out but he is really strong and capable of coping with the demands of the league and whatever is throw to him with international football.
"I have been very impressed with how he has grown in that department this season, because playing 90 minutes is a completely different role than playing just part of a game.
"I haven't seen the ceiling of Ross from a physical point of view so I am not concerned at all, but we need to manage that well and treat him like any other player."
Martinez believes the academy graduate's all-round development has been impressive since the summer.
And the way the midfielder has handled himself as the plaudits started to flood in, from winning his first England cap to a man-of-the-match display in last weekend's draw at Arsenal, has been especially encouraging.
"My biggest impression was when he arrived in pre-season and showed he was ready and desperate to have a big role in the side and since then I haven't seen a difference," added the Toffees boss.
"He takes everything in his stride and I think he is becoming a better player on a weekly basis.
"With the quality he has and his character, where he never gets fazed by the situation, he has never been affected.
"He loves the game, loves performing and I don't think the scale of the game affects him.
"If anything he is someone who, because he is so emotionally level-headed, he can play against anyone in the same manner.
"You have a big strength when you are a good listener and he has all the attributes to be a terrific footballer and it is a pleasure to work with him."
Barkley and veteran defender Sylvain Distin, whose current deal expires in the summer, are set for new contracts in January while low-key talks continue with defender Leighton Baines, who has 18 months left on his contract and is attracting interest from Manchester United.
"Even when you don't speak about issues, we work really hard behind the scenes to try to make sure that the youngsters get rewarded and Ross clearly deserves that," said Martinez.
"Sylvain has been a terrific performer this season and we couldn't be happier with his role at the club.
"All these issues are vital for us and we are going to look after them straight after this Christmas period."
Also imminent in January are additions to Martinez's squad.
They have so far coped with injuries to midfielder Darron Gibson and striker Arouna Kone (both knee) and Baines' broken toe.
However, the manager knows he must strengthen if they are to maintain their challenge for the top four, which they are just a point outside at the moment.
"We had two long-term injuries, plus suspensions and injury to Leighton Baines, but we have been able cope," Martinez said.
"It is true in January we should try to add a couple of faces just to make sure we cope with the demands of another competition, like the FA Cup, and make sure we don't get caught short in that respect, but I couldn't be happier with the strength of the squad so far.
"It doesn't matter (whether permanent or loan signings) - as long as they are through the door I don't really care.
"It is important to get the right balance. We have a strong spine at the club so it is very easy for new players to come in, but I'm not too bothered about the length of contracts of the players coming in."