"We had to lower because oil prices were going down, but now we are starting to put prices up because oil prices are starting to go up," Reuters news agency quoted al-Baker as saying after opening a new business lounge in Paris.
"Soon, I think not only Qatar Airways but most of the airlines will re-introduce the fuel surcharges because they budgeted on lower fuel price and prices are now rising rapidly," he added.
Oil prices have risen 20% in the last three months.
Qatar Airways continues to experience double-digit growth in passenger numbers, al-Baker told the agency.
Meanwhile, al-Baker said Qatar Airways was seeking strict guarantees as it talks to CFM International about supplying engines for a revamped order for Airbus narrow-body jets, which it expects to finalise "soon".
The airline has cancelled four A320neo jets powered by alternative Pratt & Whitney engines and expects to swap the overall aircraft order, which was originally for 50 jets, to larger A321neo aircraft.
CFM, a joint venture of General Electric and France's Safran, is locked in a fierce battle with Pratt & Whitney to supply engines for new Airbus medium-haul jets.
CFM exclusively supplies engines for the competing Boeing 737 aircraft, which Qatar Airways has also ordered.
According to Reuters, al-Baker acknowledged Qatar Airways had received attractive prices when it originally ordered the new Pratt & Whitney engine, but said a decision on whether to keep those or switch to CFM for the upgraded A321neo order would depend on other guarantees.
"It is a factor, but what we decide will be based on what sort of guarantees we get on deliveries and at the same time performance," he told Reuters.
Qatar Airways plans to take delivery of around 10 Airbus A350s and six Boeing 777s this year. It will also receive some Boeing 737s on behalf of Italy's Meridiana, where it hopes to tie up a deal to take a 49% stake around the end of the month.
The airline has told Boeing it is interested in taking earlier delivery of future 777-9 aircraft, because that programme is ahead of schedule, al-Baker added.
Asked if Qatar Airways could take on delivery of aircraft for airlines in which it has stakes, like BA owner IAG and Latam, he said "why not," but added he believed those airlines would take their planes as planned.
He was speaking after opening a 1,000sq m business lounge at Paris' Charles de Gaulle airport, the airline's third premium lounge abroad after London Heathrow and Dubai.
It is building further lounges in Beirut and Bangkok and is negotiating lounge space in seven other airports, al-Baker said.
The expansion comes as Gulf airlines have seen premium yields suffering due to low oil prices and rising capacity.