The Qualifications and Curriculum Authority said changes to the test - allowing pupils to gain more than half marks without having read a word of the Bard's work - were approved by Ms Morris, then Education Secretary, last year.
Her successor Charles Clarke has asked the QCA for an explanation this week after The TES revealed English teachers' unhappiness with the test. But a spokeswoman said: "The (test) changes were approved by Estelle Morris and came about following extensive consultation. QCA currently has no plans to change the ... tests."
The story sparked a heated national debate over "dumbing down" and Shakespeare's place in the curriculum, and more questions over the testing regime.
Sunday Express columnist Vanessa Feltz, a Cambridge English graduate, described the exam as "an insult to bright children and patronising to the less able".
Dr Bethan Marshall, of King's College London, has condemned the tests as a "ghastly attempt to make Shakespeare contemporary".
The revamped test, to be taken by 600,000 youngsters in May, allocates 18 of 38 marks to questions testing understanding of two scenes from one of Henry V, Twelfth Night and Macbeth.
But the writing element, worth 20 marks merely gauges pupils' linguistic and grammatical skills and, teachers argue, require no knowledge of the plays. They have condemned the changes as a bid to dumb down the curriculum.
Asked about the test at a London press conference, Mr Clarke said: "I've asked for some reports on that. I am concerned about the stories I read over the weekend. But I can't say any more until I have heard back."
Ken Boston, QCA chief executive, wrote to Mr Clarke this week to set out the regulator's position.
The controversy has heightened the opposition of many English teachers to the new KS3 tests.
Critics claim that they no longer look for literary appreciation, instead favouring bite-sized questions that merely test knowledge of grammar.
The National Union of Teachers is considering balloting for a boycott of national curriculum tests.