Both sides had multiple chances in an entertaining second half but neither side could force a breakthrough with Boro failing to score for the first time in 21 games.
The hosts had recorded clean sheets in their last two Championship outings but Ibrahima Sonko should have opened the scoring for Ipswich in the 20th minute.
Republic of Ireland international Keith Andrews fooled the Boro defence by lifting the ball into Sonko rather than shooting, but the giant centre-half directed his header wide from just four yards out.
The visitors, who have not won on their travels since the opening game of the season, had an even better chance to take the lead 11 minutes before half-time through Michael Chopra.
Carlos Edwards picked out Chopra with a right-wing cross and the striker seemed certain to volley home from three yards out, but Boro goalkeeper Carl Ikeme stood tall and the ball cannoned off him and over the bar.
Middlesbrough were struggling to carve out goalscoring opportunities despite their intricate midfield passing.
They did come close just before half-time when Barry Robson fired wide. Justin Hoyte's cross evaded Scott McDonald but Marvin Emnes worked it to Robson, and the Scot nearly picked out the bottom corner with a left-foot effort.
The Tractor Boys began the second period in the ascendancy and they completed a hat-trick of near misses when Jason Scotland struck a post in the 51st minute.
The hosts' defence backed off the forward and he unleashed a venomous drive with minimal backlift from the edge of the box which beat Ikeme at his near post but slammed against a post.
Ipswich continued to press and Jimmy Bullard's free-kick had Ikeme scrambling across his line, yet the ball went went narrowly wide.
With in-form striker Emnes having a quiet afternoon, it was McDonald who appeared intent on maintaining Boro's impressive scoring run, which had seen them net in each of the previous 20 games.
McDonald's shot from the edge of the box was turned away by Town's on-loan goalkeeper David Stockdale and Danny Collins cleared the ball away with Faris Haroun ready to pounce.
At the other end, Scotland went close again. Stockdale's long throw found Chopra and he released his strike partner but his deflected shot fell just wide.
Ipswich survived a penalty shout when the home fans thought the ball struck Lee Bowyer's hand before Sonko made a vital intervention to deny a menacing counter-attack.
The lively McDonald then had another near miss in the 81st minute, heading into the side-netting following excellent work by Hoyte.