The Dragons explained in a statement that Jackson suffered a 'non-rugby related injury on 8 April.'
"He has undergone a neck operation, which was a success, and the surgeons are satisfied with the results. Ed is making significant progress and is currently recovering," Dragons said.
Jackson, 28, signed a contract extension with the region in December.
However, he suffered a shoulder injury in February that required surgery.
Jackson has made 36 appearances for the Dragons since joining from Wasps in 2015.

Mucky Boots Nature Kindergarten will be based at Kirkton of Maryculter woods.
It will have space for 15 children between the ages of three and five.
Manager Dawn Ewan told the BBC Scotland website there were many benefits and explained: "It is a massive woodland and children are generally happier to be outside."
There have been outdoor nurseries across Scotland - including in Glasgow, Fife and Perthshire - for many years, but Mucky Boots is understood to be the first such venture in that part of Scotland.
The idea originated in Scandinavia several decades ago.
Mrs Ewan, a mother-of-two in her 30s, said: "My background is teaching. This outdoor nursery has been a pipedream for about 15 years and then we found this woodland.
"We have visited various ones in Scotland and were really impressed."
On the benefits of an outdoor nursery for children, she said: "We are looking to build up their confidence, and that's the feedback we've had from the pilot sessions.
"It increases their resilience, they are able to problem solve better, and it's good for emotional development and physical health too.
"Children will have freedom to explore, with a true connection to the natural world.
"They will be more ready for school."
Climbing hills and using open fires are among the type of activities at the nursery.
There will be three staff for the 15 children due to what Mrs Ewan accepted was a "higher-risk environment".
She said: "We want to do this right - it needs to be good quality."
For adverse weather situations, there is a teepee and sheltered areas, and they also have use of a Scout hut for extreme weather situations.
Mrs Ewan added: "We have only used the indoor space twice in two years.
"As the saying goes, there's no such thing as bad weather, but inappropriate clothes. That's our motto."
She said the nursery had registered with the Care Inspectorate and would work with Aberdeenshire Council.

26 September 2016 Last updated at 14:43 BST
She's come back from the Paralympics in Rio with four medals, including gold in the 400m, a silver in the 4x100m relay - and not to mention her gold medal and new world record in the 500m cycling time trial!
Winning a gold medal in the sprinting and again in the cycling, Kadeena is the first British Paralympian to top the podium in two different sports since 1984.
So plenty of reasons for her to be pleased and what better way to celebrate winning gold than with a little bit of a dance?
Kadeena shows Newsround's Naz how to celebrate like a pro.
Newport Gwent Dragons forward Ed Jackson is recovering in hospital after undergoing surgery for a neck injury.
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A fully outdoor nursery, believed to be the first in Aberdeenshire, is due to open in April after a successful two-year pilot.
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Kadeena Cox is no stranger to celebrating on the podium, the 25-year-old from Leeds has enjoyed a lot of success in her career.