The dub first aired on BabyTV, an Israeli channel for young kids, in September 2004. It was a part of the channel's regular lineup until mid-2010. (source 1,source 2)
BabyTV's website had two different pages for the show, both with videos of the Hebrew intro. The original show page featured some activities based on the show, like printable googly eyes to make homemade Oobi puppets. (source) The newer show page only featured a video. (source) The page stayed on the website until 2021, many years after the show stopped airing in Israel.
The dub also aired on Nickelodeon Israel from 2008 to 2011. On Nick Israel, the show started airing in early 2008. From April to mid-June, it was shown on Saturdays at 7:45 and 8:22 AM. (source) From June until August 31, it was shown daily at 7:45 AM. (source)
In September 2008, the show started airing at different times on weekdays: once at 8:10 AM on Mondays, and twice at 8:10 and 9:15 AM from Tuesday to Friday. (source)
This schedule continued throughout 2009, with some changes depending on holidays/events. On certain days, the timeslot was changed to two airings at 6:55 and 7:35 AM. (source) In 2010, Oobi was only shown at 9:15 AM each day. (source) It was taken off the schedule sometime in mid-2011.
The episodes were dubbed by NLS Studios, a major dubbing company in Tel Aviv, Israel. Credits for the dub can be found on Ishim, a catalog of Hebrew shows.
From BabyTV:אובי וחבריו הם בובות, המשוחקות על ידי ידיים המאובזרות בעיניים. הם חיים בבית ומתפקדים כמשפחה אנושית לכל דבר. הם משחקים, לומדים, משתוללים וצוחקים ממש כמו ילדים. החוויות והמשחקים שלהם לקוחים מעולם הפעוטות ומעוררים את הזדהות הצופים דרך ההומור והנגיעה ביומיומי והמוכר.
Translation:Oobi and his friends are puppets, played by hands outfitted with eyes. They live at home and act like a human family in every respect. They play, learn, go wild, and laugh just like children. Their experiences and games are taken from the world of toddlers and strike a chord with viewers through humor and daily familiarities.
All of the long-form episodes were dubbed in Hebrew. As with most dubs, the shorts weren't dubbed or shown in Israel.