The minority investment, said IAG on Thursday (April 12), was made with a view to initiating discussions with Norwegian, including the possibility of a full offer.
IAG has, however, confirmed no such talks have yet taken place.
67.5% of shares in Norwegian are currently available on the open market.
In a statement, IAG said: "IAG considers Norwegian to be an attractive investment and has acquired a 4.61 per cent ownership position in the airline (minority investment).
"The minority investment is intended to establish a position from which to initiate discussions with Norwegian, including the possibility of a full offer for Norwegian.
"IAG confirms that no such discussions have taken place to date, that it has taken no decision to make an offer at this time and that there is no certainty that any such decision will be made.
"A further announcement will be made if appropriate."
IAG already owns British Airways, Iberia, Aer Lingus and budget brands Vueling and Level.
Norwegian would be a good fit for IAG, which launched low cost long-haul airline Level at Barcelona, which is a Norwegian base. Barcelona is also the home of IAG’s short-haul budget airline Vueling.
At Gatwick, IAG would be able to control Norwegian’s expansion in long-haul, which has bitten into BA’s traffic there. It looks likely that all three budget brands would be combined under one name.
Following the announcement, Norwegian’s shares were up 22% on the Norwegian exchange at 11am.
Norwegian posted a £27.4 million loss in 2017 and has issued a profits warning for the first quarter of 2018.
Its share price has plummeted from about £26 in January 2017 to around £16 on Thursday, making a takeover potentially very cheap.
The carrier was forced to raise £119 million in new funds in March and will increase capacity by 40% this year with the arrival of nine more long-haul aircraft.
A Norwegian spokesperson said: "Norwegian has just been made aware that the International Airline Group (IAG) has acquired of 4.6 percent of the shares in Norwegian Air Shuttle ASA.
"Norwegian had no prior knowledge of this acquisition before it was reported by the media mid-morning Thursday.
"Norwegian has not been in any discussions or dialogue with IAG about the matter.
"Norwegian believes that interest from one of the largest international aviation groups demonstrates the sustainability and potential of our business model and global growth.
"The company has no further comments at this stage."
