Justice Isaac Lenaola said an immediate move to digital would be unfair to Kenyans keen to follow the polls on TV.
The Communications Commission of Kenya (CCK) had wanted to turn it off last month, ahead of a 2015 global deadline.
But a consumer group challenged its decision, arguing that Kenyans had not been given enough time to prepare.
According to Kenya's Daily Nation newspaper, the Consumer Federation of Kenya (Cofek) said the first notice about the analogue signal switch-off, planned for 31 December 2012, was given on 7 December 2012.
The cost of set-top boxes needed to receive digital transmissions meant it would be prohibitively expensive for most Kenyans, Cofek argued.
Last month, the chairman of Kenya's Media Owners Association, Kiprono Kittony, said the switch-off would affect four million people - and also urged the government to reconsider the date.
Judge Lenaola told the CCK and Cofek to agree on a new date, which he felt should be after the March 2013 elections.
The last elections in December 2007 were highly contentious in Kenya, where television is the main news source in cities and towns.
Allegations of electoral fraud following the results ignited ethnic tensions, leading to the deaths of some 1,300 people and forcing some 600,000 from their homes.
The judge ordered the two organisations to appear before him on 20 February should they fail to agree on a new date.
Neighbouring Tanzania went ahead with its digital migration on 31 December, the first to do so of the five members of the East African Community, which had agreed to an early switchover to fix any glitches ahead of the June 2015 global deadline to end analogue transmissions.