Jackson beat Wycombe boss Peter Taylor, Chesterfield's Lee Richardson and Darlington's Dave Penney to receive the award for the second time this year, having also received the accolade in February, shortly before undergoing cancer treatment.
He admitted: "That was a sad one because I won manager of the month and then I went to hospital and didn't know if I was going to be coming back to the club.
"A lot of hard work's gone in over the summer and it's been rewarded with this today."
The Championship award went to Dave Jones of Cardiff City, while Bristol Rovers' Paul Trollope received the League One award.
It could be a double celebration for Lincoln, with midfielder Lee Frecklington one of four contenders for the League Two player of the month award.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.