The handset (pictured), worth nearly £24, will have airtime added in four bi-weekly top-ups of £5. There is a limit of two handsets per customer.
The MVNO is also considering hiring extra staff in larger stores to cope with demand. The offer ends when all 40,000 have been given away.
Asda head of mobile Ted Cadogan said: “Christmas is the time when we think of our loved ones and we’re delighted to be able to help our customers stay in touch for less.”