The first lady's longtime friend, Paolo Zampolli, told Associated Press she thinks Melania Trump "wanted to spend some quality time with her family".
The first lady's spokesperson, Stephanie Grisham, told DailyMail.com that Melania Trump has been meeting with her staff on the "Be Best" initiative and working on upcoming projects like the annual White House congressional picnic and Fourth of July plans.
Grisham told the AP the first lady would like to be "out and about promoting her initiatives" but "her health comes first".
A reporter for Huffington Post compared Melania's tweet on Wednesday to previous tweets from the president and wondered: "Where have we heard' this before?
Huffington Post notes "working " is a favourite idiom used by the president, particularly in regards to talking about the media.
"The Fake News is working overtime," President Trump wrote in a May 9 tweet.
Trump also likes to talk about how hard Republicans, his administration and he works.
In this February 16 tweet on immigration talks, he noted: "Republicans are still working hard."
And "On behalf of the American people" is another favourite Trump phrase, which he used on May 10 to welcome home the hostages from North Korea, the last time Melania Trump was seen in public.
Some celebrities are having fun with the speculation on where the US first lady's been hiding.
Comedian Sarah Silverman retweeted Melania's tweet with her own comment: "Who is this? where's Melania?"
Holly Figueroa O'Reilly, who calls herself a Grammy losing songwriter, mom of five, and one of the national organisers of the "March for Truth", joined in the speculation about who wrote Melania's tweet.
"There is a 0.00000% chance Melania wrote this tweet. Weird grammar and syntax? Exclamation marks? Sounds familiar. I can't quite put my tiny orange finger on it," she wrote on Twitter.
Author Brian Klass agreed, tweeting: "Yeah, so I don't think Melania wrote that 'working overtime' tweet."
There's also a notable lack of photos of the first lady with no pictures being posted of her meetings with staff or of her "working hard".
Melania Trump herself has posted videos on social media of her work, such as one posted about the White House holiday decorations in December and another on her preparations for the first state dinner in April.
But there has been nothing about her recently, leading to questions about why she spent a week in the hospital for an embolisation procedure and her prolonged recovery at home.
First ladies are under no obligation to release updates on their health. But there have been questions about Melania's long absence for a procedure medical experts say involves a quick recovery.
A reporter for CNBC tweeted he saw the first lady in the West Wing on Tuesday walking with aides. No other details were given.
Politico reported Wednesday there are a variety of conspiracy theories being banded about given Melania's absence: She's moved back to New York City, she's co-operating with special counsel Robert Mueller, she's living with the Obamas, working on a tell-all book or she had a secret nip and tuck that she's healing from.
President Trump said last week the first lady is "doing great" after her kidney surgery.
"She's doing great. Right there. She's doing great," he said on the White House lawn last Friday morning before he left to give the commencement address at the US Naval Academy in Annapolis, Maryland.
"She's looking at us, right there," he added and pointed to a window in the White House residence above him.
The first lady was not visible to reporters on the ground.
