The seven-times' world champion shared the first two frames with Milkins in the first round of the ranking tournament in China, but lost the next four frames. He faces losing his spot in the world's top 16 for the first time in 23 years when the new list is drawn up.
The consequences of Hendry's loss means he will have to qualify for the UK Championship in December - the second most coveted ranking tournament on the circuit behind the World Championship.
His absence from the Masters in London in January - a tournament only open to the world's top 16 - may hurt him more having won the prestigious event a record six times.
A 42 from Hendry in the second frame was enough to cancel out an opening 73 from Milkins before runs of 47, 73 and 49 helped the English player complete a comfortable win.
Defending Masters champion Ding Junhui lost 5-3 to Martin Gould. The home favourite won the first three frames, but lost the next five as Gould secured a meeting with Matthew Stevens, who was rarely troubled in downing Stephen Lee 5-2.
Mark Williams and John Higgins wasted little time in easing themselves into the last 16 of the Shanghai Masters with assured displays in the first round.
World number one Williams thumped Andrew Higginson 5-0, while world champion Higgins had few problems in completing a 5-2 victory over Mark Davis.
Higgins will face Stuart Bingham on Thursday for a place in the last eight after the new Australian Open champion continued his recent good form with a 5-1 drubbing of World Championship runner-up Judd Trump.
Michael Holt is also through to the last 16 after accounting for the 2006 world champion Graeme Dott with a 5-2 victory. He will face another world champion in the form of Neil Robertson after the 2010 champion dismissed Liang Wenbo's hopes with a 5-1 win.
Williams was quickly into his stride against Higginson - who is best known for his run to the final of the Welsh Open in 2007 - as runs of 77, 37 and 41 helped him establish a 4-0 lead at the mid-session interval against an opponent who was clearly struggling with the pace of the table.
Higginson opened with a 54 in the fifth frame, but could not prevent the whitewash as Williams cleared the table with his own 54 to nick the frame by two points.
Williams will face Milkins in the last 16.
Higgins opened with a run of 112 against Davis only for his opponent to seize upon a missed red by the Scotsman in the second frame on a break of 47. Davis cleared with a 76, but that was as good as good as it was to get for a player ranked at 15th in the world as Higgins won the next two aided by a run of 84 in the fourth frame.
The pair split the next two pretty forgettable frames in which both men spurned chances - Davis making 46 and 42 in the sixth frame - before Higgins closed out the match with a timely run of 68 in the seventh frame.
He is likely to face a tough test against the in-form Bingham, who brushed aside Trump with knocks of 129, 112, 48, 37 and 55. Trump's only slice of joy was a break of 96 in the fourth frame.
Holt ran in breaks of 54, 83 and 72 to progresses with Dott's top efforts of 56 and 58 giving him brief hope as he recovered from 0-3 to 2-3 before his opponent won the final two frames of the match.