Motion has written three poems for royal occasions
Titled The Younger Sister, it also points out that Margaret, who was being buried in Windsor on Friday, died with the knowledge that "love and duty speak two languages".
Motion, who became poet laureate in 1999, has written two previous sets of verse to mark royal occasions - for the Queen Mother's 100th birthday and Prince Edward's wedding.
The poet laureate's job is to write verse on major royal and national events.
Click here to read The Younger Sister
"Quite what the laureate is and is not expected to write about is as mysterious to me as it is to everybody else," he told BBC News Online.
"But there is an additional expectation that they will write about traditional events in the royal calendar.
"It seemed to me that in all kinds of ways this was a significant thing and should be written about."
The poem would be seen by the Queen and the Prince of Wales before the funeral, the Independent newspaper reported.
It has also been hailed as the start of a new generation of "realistic" royal verse.
Motion, who is also a professor of creative writing at the University of East Anglia, also wrote a poem in the wake of 11 September.
The Younger Sister
By Andrew Motion
"The luxuries, of course, and privilege -
The money, houses, holidays, the lot:
All these were real, and all these drove a wedge
Between your life and ours. And yet the thought
Of how no privilege on earth can keep
A life from suffering in love and loss -
This means we turn to you and see how deep
The current runs between yourself and us.
And now death spells it out again, and more,
As it becomes your final human act:
A daughter gone before her mother goes;
A younger sister heading on before;
A woman in possession of the fact
That love and duty speak two languages."