The move comes days after e& said it was looking to expand into new markets in Africa, Europe and Asia and in areas outside telecoms such as financial technology as its seeks to drive growth.
Vodafone, like all mobile operators, has been struggling in its more mature markets, where competition and regulation have pushed prices lower.
Net debt at the group has reached 44.3 billion euros, and its Chief Executive Nick Read is under pressure to simplify its portfolio and improve returns after a more than 20% slide in its share price since he took over in 2018.
Vodafone was not immediately available for comment.
United Arab Emirates-based e& said it had made the investment to gain "significant exposure to a world leader in connectivity and digital services".
e& said it had no intention of making an offer to buy Vodafone, saying it is fully supportive of the company's current business strategy and its board and existing management team.
"We see this investment as a good opportunity for e& and its shareholders as it will allow us to enhance and develop our international portfolio, in line with our strategic ambition," said CEO Hatem Dowidar.
The UAE firm recently separated its business into consumer services-focused e& life, e& enterprise, providing digital services to government and business, and telecoms arm Etisalat, which its CEO said is the world's seventh largest by market capitalisation.